Question 1

Use the properties of equality to solve the equation. $$\frac { 11 } { 12 } a = \frac { 1 } { 3 }$$

Accepted Answer

B

Question 2

Solve the equation. $$2 x + 4 + 7 x = 3 x + 2 x - 32$$

Accepted Answer

Combining like terms on both sides gives $9x + 4 = 5x - 32$. Subtracting $5x$ and $4$ from both sides gives $4x = -36$, so $x = -9$.

Question 3

Solve the equation. 0.11 t - 2.1 = 0.06 t - 0.3

Accepted Answer

To solve for t, we need to get all the t terms on one side and all the constant terms on the other side.

0.11 t - 2.1 = 0.06 t - 0.3

First, let's get rid of the decimal points by multiplying everything by 100:

11t - 210 = 6t - 30

Next, let's isolate the t terms:

11t - 6t = 210 - 30

5t = 180

Finally, let's solve for t:

t = 36

Therefore, the solution is t = 36, which is choice C.

Question 4

Solve the equation. n + 0.5 n = 90

Accepted Answer

Combining like terms on the left side of the equation, we get 1.5n = 90.
Dividing both sides by 1.5, we get n = 60. Therefore, the answer is D, n = 60.

Question 5

Use a property of equality to solve the equation. $$\frac { 4 } { 3 } = - \frac { 17 } { 3 } + x$$

Accepted Answer

To solve for $x$, add $\frac{17}{3}$ to both sides of the equation: $\frac{4}{3} + \frac{17}{3} = x$, which simplifies to $\frac{21}{3} = x$, or $7 = x$.

Question 6

When two lines intersect as in the illustration below, four angles are formed. Angles that are side-by-side, such as $\angle 1$ and $\angle 2$ , are called adjacent angles. Angles that are nonadjacent, such as $\angle 1$ and $\angle 3$ or $\angle 2$ and $\angle 4$ , are called vertical angles. From geometry, we know that if two lines intersect, vertical angles have the same measure. If $m ( \angle 1 ) = ( 5 x + 10 ) ^ { \circ }$ and $m ( \angle 3 ) = ( 7 x - 10 ) ^ { \circ }$ , find x . Read $m ( \angle 1 )$ as "the measure of $\angle 1$ ".

Accepted Answer

Since $\angle 1$ and $\angle 3$ are vertical angles, they have the same measure. Setting the two expressions for their measures equal to each other and solving for x, we get: 
$$(5x + 10)^\circ = (7x - 10)^\circ$$
$$5x + 10 = 7x - 10$$
$$20 = 2x$$
$$x = 10$$
Therefore, the answer is choice E.

Question 7

Use an equation to solve the problem. Sales tax on a $14 compact disc is $0.84. At what rate is sales tax computed?

Accepted Answer

The sales tax rate can be found by dividing the tax amount by the price of the item and then converting it to a percentage. So, $0.84 / $14 = 0.06, which is 6% when converted to a percentage.

Question 8

Solve the equation. If the equation is an identity or a contradiction, so indicate. 8 x - 2(5 x + 4)= 2( x + 5)

Accepted Answer

The answer of Solve the equation. If the equation is...

Question 9

Use an algebraic approach to solve the problem: Find a number such that one-half of the number is 5 less than two-thirds of the number.

Accepted Answer

The answer of Use an algebraic approach to solve the...

Question 10

The amount A in an account is given by the formula A = p + i where p is the principal and i is the interest. How much interest was earned if an original deposit (the principal)of $4,250 has grown to be $4,520?

Accepted Answer

The interest earned is calculated by subtracting the original principal from the total amount after interest has been added. So, $4,520 - $4,250 = $270.

Question 11

Eva invested a certain amount of money at 13% interest and $2,500 more than that amount at 15%. Her total yearly interest was $1,775. How much did she invest at each rate?

Accepted Answer

Let the amount invested at 13% be x dollars. Then, the amount invested at 15% is x + $2,500. The total interest from both investments is $1,775, which can be represented by the equation: 0.13x + 0.15(x + 2500) = 1775. Solving this equation gives x = $5,000 for the 13% investment and x + $2,500 = $7,500 for the 15% investment.

Question 12

Solve the equation. 0.43 x + 0.4(8,000 - x )= 3350

Accepted Answer

To solve the equation, distribute and simplify: 0.43x + 0.4(8000 - x) = 3350. This simplifies to 0.43x + 3200 - 0.4x = 3350. Combining like terms gives 0.03x = 150. Dividing both sides by 0.03 gives x = 5000.

Question 13

Use the properties of equality to solve the equation. $p - \frac { 2 } { 5 } = \frac { 1 } { 3 }$

Accepted Answer

To solve for $p$, add $\frac{2}{5}$ to both sides of the equation to isolate $p$: $p = \frac{1}{3} + \frac{2}{5}$. Finding a common denominator (15) for the fractions gives $p = \frac{5}{15} + \frac{6}{15} = \frac{11}{15}$.

Question 14

Solve the equation. $\frac { h } { 7 } + \frac { h } { 8 } = 1$

Accepted Answer

To solve the equation, we first need to find a common denominator for the two fractions. The smallest common multiple of 7 and 8 is 56. Therefore, we can rewrite the equation as:

\begin{align*}
\frac{h}{7}+\frac{h}{8}&=1\
\frac{8h}{56}+\frac{7h}{56}&=1\
\frac{15h}{56}&=1\
15h&=56\
h&=\frac{56}{15}\
\end{align*}

Therefore, the answer is D.

Question 15

Use an algebraic approach to solve the problem: Suppose that the width of a certain rectangle is 2 inch more than one-fourth of its length. The perimeter of the rectangle is 24 inches. Find the length and width of the rectangle.

Accepted Answer

The perimeter of a rectangle is given by $2l + 2w = 24$, where $l$ is the length and $w$ is the width. Given $w = \frac{1}{4}l + 2$, substituting the width's expression into the perimeter equation gives $2l + 2(\frac{1}{4}l + 2) = 24$. Solving this equation for $l$ gives $l = 8$ inches. Substituting $l = 8$ inches back into $w = \frac{1}{4}l + 2$ gives $w = 4$ inches. Therefore, the rectangle is 4 inches wide and 8 inches long.

Question 16

Use an algebraic approach to solve the problem: A board 20 feet long is cut into two pieces such that the length of one piece is two-thirds of the length of the other piece. Find the length of the shorter piece of board.

Accepted Answer

Let the length of the shorter piece be $x$ feet. Then, the length of the longer piece is $\frac{2}{3}x$ feet. Since the total length of the board is 20 feet, we have $x + \frac{2}{3}x = 20$. Solving for $x$, we find that $x = 8$ feet, making the shorter piece 8 feet long.

Question 17

Use a property of equality to solve the equation. $$\frac { y } { 18 } = - 8$$

Accepted Answer

To solve the equation $\frac{y}{18} = -8$, use the multiplication property of equality by multiplying both sides by 18 to isolate $y$. This gives $y = 18 \times -8 = -144$.

Question 18

Use an equation to solve the problem. The average price of homes in one neighborhood decreased 8% since last year, a drop of $5,400. What was the average price of a home last year?

Accepted Answer

The answer of Use an equation to solve the problem....

Question 19

Solve the equation. 5( t - 2)+ 2( t - 1)= -2( t - 1)+ 10( t + 2)

Accepted Answer

First, distribute the numbers in the equation: 5(t - 2) + 2(t - 1) = -2(t - 1) + 10(t + 2) becomes 5t - 10 + 2t - 2 = -2t + 2 + 10t + 20. Simplify both sides: 7t - 12 = 8t + 22. Rearrange to solve for t: 7t - 8t = 22 + 12, which simplifies to -t = 34, so t = -34.

Question 20

Solve the equation. $$7 x - 15 + 6 x - 10 x + 9 = 24$$

Accepted Answer

The answer of Solve the equation. \[7 x - 15...

Quiz 2: Equations, Inequalities, and Problem Solving

Use the properties of equality to solve the equation. $\frac { 11 } { 12 } a = \frac { 1 } { 3 }$

Solve the equation. $2 x + 4 + 7 x = 3 x + 2 x - 32$

Solve the equation. 0.11 t - 2.1 = 0.06 t - 0.3

Solve the equation. n + 0.5 n = 90

Use a property of equality to solve the equation. $\frac { 4 } { 3 } = - \frac { 17 } { 3 } + x$

Use an equation to solve the problem. Sales tax on a $14 compact disc is $0.84. At what rate is sales tax computed?

Solve the equation. If the equation is an identity or a contradiction, so indicate. 8 x - 2(5 x + 4) = 2( x + 5)

Use an algebraic approach to solve the problem: Find a number such that one-half of the number is 5 less than two-thirds of the number.

The amount A in an account is given by the formula A = p + i where p is the principal and i is the interest. How much interest was earned if an original deposit (the principal) of $4,250 has grown to be $4,520?

Eva invested a certain amount of money at 13% interest and $2,500 more than that amount at 15%. Her total yearly interest was $1,775. How much did she invest at each rate?

Solve the equation. 0.43 x + 0.4(8,000 - x ) = 3350

Use the properties of equality to solve the equation. $p - \frac { 2 } { 5 } = \frac { 1 } { 3 }$

Solve the equation. $\frac { h } { 7 } + \frac { h } { 8 } = 1$

Use an algebraic approach to solve the problem: Suppose that the width of a certain rectangle is 2 inch more than one-fourth of its length. The perimeter of the rectangle is 24 inches. Find the length and width of the rectangle.

Use an algebraic approach to solve the problem: A board 20 feet long is cut into two pieces such that the length of one piece is two-thirds of the length of the other piece. Find the length of the shorter piece of board.

Use a property of equality to solve the equation. $\frac { y } { 18 } = - 8$

Use an equation to solve the problem. The average price of homes in one neighborhood decreased 8% since last year, a drop of $5,400. What was the average price of a home last year?

Solve the equation. 5( t - 2) + 2( t - 1) = -2( t - 1) + 10( t + 2)

Solve the equation. $7 x - 15 + 6 x - 10 x + 9 = 24$

Quiz 2: Equations, Inequalities, and Problem Solving

Use the properties of equality to solve the equation. 1112a=13\frac { 11 } { 12 } a = \frac { 1 } { 3 }1211​a=31​

Solve the equation. 2x+4+7x=3x+2x−322 x + 4 + 7 x = 3 x + 2 x - 322x+4+7x=3x+2x−32

Solve the equation. 0.11 t - 2.1 = 0.06 t - 0.3

Solve the equation. n + 0.5 n = 90

Use a property of equality to solve the equation. 43=−173+x\frac { 4 } { 3 } = - \frac { 17 } { 3 } + x34​=−317​+x

Use an equation to solve the problem. Sales tax on a $14 compact disc is $0.84. At what rate is sales tax computed?

Solve the equation. If the equation is an identity or a contradiction, so indicate. 8 x - 2(5 x + 4) = 2( x + 5)

Use an algebraic approach to solve the problem: Find a number such that one-half of the number is 5 less than two-thirds of the number.

The amount A in an account is given by the formula A = p + i where p is the principal and i is the interest. How much interest was earned if an original deposit (the principal) of $4,250 has grown to be $4,520?

Eva invested a certain amount of money at 13% interest and $2,500 more than that amount at 15%. Her total yearly interest was $1,775. How much did she invest at each rate?

Solve the equation. 0.43 x + 0.4(8,000 - x ) = 3350

Use the properties of equality to solve the equation. p−25=13p - \frac { 2 } { 5 } = \frac { 1 } { 3 }p−52​=31​

Solve the equation. h7+h8=1\frac { h } { 7 } + \frac { h } { 8 } = 17h​+8h​=1

Use an algebraic approach to solve the problem: Suppose that the width of a certain rectangle is 2 inch more than one-fourth of its length. The perimeter of the rectangle is 24 inches. Find the length and width of the rectangle.

Use an algebraic approach to solve the problem: A board 20 feet long is cut into two pieces such that the length of one piece is two-thirds of the length of the other piece. Find the length of the shorter piece of board.

Use a property of equality to solve the equation. y18=−8\frac { y } { 18 } = - 818y​=−8

Use an equation to solve the problem. The average price of homes in one neighborhood decreased 8% since last year, a drop of $5,400. What was the average price of a home last year?

Solve the equation. 5( t - 2) + 2( t - 1) = -2( t - 1) + 10( t + 2)

Solve the equation. 7x−15+6x−10x+9=247 x - 15 + 6 x - 10 x + 9 = 247x−15+6x−10x+9=24

Use the properties of equality to solve the equation. $\frac { 11 } { 12 } a = \frac { 1 } { 3 }$

Solve the equation. $2 x + 4 + 7 x = 3 x + 2 x - 32$

Use a property of equality to solve the equation. $\frac { 4 } { 3 } = - \frac { 17 } { 3 } + x$

Use the properties of equality to solve the equation. $p - \frac { 2 } { 5 } = \frac { 1 } { 3 }$

Solve the equation. $\frac { h } { 7 } + \frac { h } { 8 } = 1$

Use a property of equality to solve the equation. $\frac { y } { 18 } = - 8$

Solve the equation. $7 x - 15 + 6 x - 10 x + 9 = 24$