Question 1

Solve the equation.
-$\frac { 1 } { 5 } ( x + 6 ) = \frac { 1 } { 7 } ( x + 8 )$

Accepted Answer

The answer of Solve the equation.
-\(\frac { 1 } {...

Question 2

Write the algebraic expression described. Simplify if possible.
-In the race for Student Body President, Jose received 157 more votes than Angela. If Angela received x votes, how many votes did Jose receive?

Accepted Answer

Jose received x votes plus an additional 157, so the expression is x + 157.

Question 3

Solve the equation.
-$7 x - ( 3 x - 1 ) = 2$

Accepted Answer

First, distribute the negative sign inside the parentheses: $7x - 3x + 1 = 2$. Combine like terms: $4x + 1 = 2$. Subtract 1 from both sides: $4x = 1$. Divide by 4: $x = \frac{1}{4}$.

Question 4

Solve.
-A pharmacist is asked to give a customer $7.5$ milliliters of an antibiotic over a period of 8 hours. If the antibiotic is to be given every 4 hours starting immediately, how much antibiotic should be given in each dose?

Accepted Answer

The total amount of antibiotic to be given is $7.5$ milliliters over $8$ hours. Since the antibiotic is to be given every $4$ hours, there will be $2$ doses in $8$ hours ($8 \div 4 = 2$). Therefore, each dose should be $7.5 \div 2 = 3.75$ milliliters.

Question 5

Solve the equation.
-$13 ( 5 x - 7 ) = 3 x - 5$

Accepted Answer

First, distribute the 13 across the terms inside the parentheses: $13(5x) - 13(7) = 3x - 5$, which simplifies to $65x - 91 = 3x - 5$. Then, subtract $3x$ from both sides to get $62x - 91 = -5$. Adding 91 to both sides gives $62x = 86$. Finally, divide both sides by 62 to solve for $x$, which gives $x = \frac{86}{62}$, which simplifies to $x = \frac{43}{31}$.

Question 6

Write the algebraic expression described. Simplify if possible.
-If x represents the first of three consecutive odd integers, express the sum of the three integers in terms of x.

Accepted Answer

The three consecutive odd integers can be represented as x, x + 2, and x + 4. Their sum is x + (x + 2) + (x + 4) = 3x + 6.

Question 7

Write the algebraic expression described. Simplify if possible.
-A quadrilateral is a four-sided figure whose angle sum is $360 ^ { \circ }$. If one angle measures $x ^ { \circ }$, a second angle measures $2 x ^ { \circ }$, and a third angle measures $9 x ^ { \circ }$, express the measure of the fourth angle in terms of $x$.

Accepted Answer

The sum of the angles in a quadrilateral is $360^\circ$. The sum of the given angles is $x + 2x + 9x = 12x$. Therefore, the fourth angle is $360 - 12x$.

Question 8

Solve the equation.
-$9 y = 8 ( 4 y - 3 )$

Accepted Answer

To solve the equation $9y = 8(4y - 3)$, distribute the 8 on the right side to get $9y = 32y - 24$. Then, subtract $32y$ from both sides to get $-23y = -24$. Finally, divide both sides by $-23$ to solve for $y$, which gives $y = \frac{24}{23}$.

Question 9

Solve the equation.
-$6 ( 3 x - 1 ) = 24$

Accepted Answer

First, distribute the 6: $6 \times 3x - 6 \times 1 = 18x - 6$. Set the equation to $18x - 6 = 24$. Add 6 to both sides to get $18x = 30$. Divide both sides by 18 to solve for $x$, resulting in $x = \frac{30}{18} = \frac{5}{3}$.

Question 10

Write the algebraic expression described. Simplify if possible.
-If x is the first of three consecutive integers, express the sum of 22 and the third integer as an algebraic expression in terms of x.

Accepted Answer

The answer of Write the algebraic expression described. Simplify if...

Question 11

Write the algebraic expression described. Simplify if possible.
-If x represents the first of four consecutive even integers, express the sum of the first integer and the fourth integer in terms of x.

Accepted Answer

The first integer is x, the second is x+2, the third is x+4, and the fourth is x+6. The sum of the first and fourth integers is x + (x + 6) = 2x + 6.

Question 12

Write the algebraic expression described. Simplify if possible.
-Two numbers have a sum of 60. If one number is q, express the other number in terms of q.

Accepted Answer

The sum of two numbers is 60, so if one number is q, the other number must be 60 - q to add up to 60.

Question 13

Solve the equation.
-$0.4 x - 0.6 x - 5 = 3$

Accepted Answer

Combining like terms gives $-0.2x = 8$, and solving for $x$ gives $x = -40$.

Question 14

Solve the equation.
-$3 n = 5 ( 5 n + 8 )$

Accepted Answer

To solve the equation $3n = 5(5n + 8)$, first distribute the 5 on the right side: $3n = 25n + 40$. Then, move all terms involving $n$ to one side: $3n - 25n = 40$, which simplifies to $-22n = 40$. Finally, divide both sides by -22 to solve for $n$, resulting in $n = -\frac{40}{22}$, which simplifies to $-\frac{20}{11}$.

Question 15

Solve the equation.
-$- 10.4 z + 1.6 = - 42.9 - 1.5 z$

Accepted Answer

To solve the equation $- 10.4 z + 1.6 = - 42.9 - 1.5 z$, first combine like terms by adding $10.4z$ to both sides and adding $42.9$ to both sides to get $1.6 + 42.9 = 8.9z$. Simplifying the left side gives $44.5 = 8.9z$. Dividing both sides by $8.9$ gives $z = 5$.

Question 16

Write the algebraic expression described. Simplify if possible.
-The sum of the angles of a triangle is $180 ^ { \circ }$. If one angle of a triangle measures $x ^ { \circ }$ and a second angle measures $( 9 x + 18 ) ^ { \circ }$, express the measure of the third angle in terms of $x$.

Accepted Answer

The sum of the angles of a triangle is $180 ^ { \circ }$. So, the third angle is $180 ^ { \circ } - x ^ { \circ } - ( 9 x + 18 ) ^ { \circ }$. Simplifying, we get $180 ^ { \circ } - x ^ { \circ } - 9 x - 18 ^ { \circ }$, which is equal to $162 ^ { \circ } - 10 x ^ { \circ }$.

Question 17

Solve the equation.
-$\frac { 1 } { 4 } ( x + 12 ) + \frac { 1 } { 6 } ( x + 6 ) = x + 8$

Accepted Answer

To solve the equation, first clear the fractions by multiplying through by 12 (the least common multiple of 4 and 6). This gives: 3(x + 12) + 2(x + 6) = 12(x + 8). Simplifying, we get 3x + 36 + 2x + 12 = 12x + 96. Combine like terms: 5x + 48 = 12x + 96. Rearrange to get: 5x - 12x = 96 - 48, which simplifies to -7x = 48. Solving for x gives x = -48/7.

Question 18

Write the algebraic expression described. Simplify if possible.
-A 21-centimeter piece of rope is cut into two pieces. If one piece is z centimeters long, express the other length as an algebraic expression in z.

Accepted Answer

The total length of the rope is 21 cm. If one piece is z cm long, the other piece must be the total length minus this piece, which is expressed as (21 - z) cm.

Question 19

Solve the equation.
-$( y - 8 ) - ( y + 2 ) = 5 y$

Accepted Answer

The answer of Solve the equation.
-\(( y - 8 )...

Question 20

Write the algebraic expression described. Simplify if possible.
-During a walk-a-thon, Rosilyn walked 18 fewer laps than June walked. If June walked b laps, how many laps did Rosilyn walk?

Accepted Answer

Rosilyn walked 18 fewer laps than June, so if June walked $b$ laps, Rosilyn walked $b - 18$ laps.

Quiz 2: Equations, Inequalities, and Problem Solving

Solve the equation. - $\frac { 1 } { 5 } ( x + 6 ) = \frac { 1 } { 7 } ( x + 8 )$

Write the algebraic expression described. Simplify if possible. -In the race for Student Body President, Jose received 157 more votes than Angela. If Angela received x votes, how many votes did Jose receive?

Solve the equation. - $7 x - ( 3 x - 1 ) = 2$

Solve. -A pharmacist is asked to give a customer $7.5$ milliliters of an antibiotic over a period of 8 hours. If the antibiotic is to be given every 4 hours starting immediately, how much antibiotic should be given in each dose?

Solve the equation. - $13 ( 5 x - 7 ) = 3 x - 5$

Write the algebraic expression described. Simplify if possible. -If x represents the first of three consecutive odd integers, express the sum of the three integers in terms of x.

Solve the equation. - $9 y = 8 ( 4 y - 3 )$

Solve the equation. - $6 ( 3 x - 1 ) = 24$

Write the algebraic expression described. Simplify if possible. -If x is the first of three consecutive integers, express the sum of 22 and the third integer as an algebraic expression in terms of x.

Write the algebraic expression described. Simplify if possible. -If x represents the first of four consecutive even integers, express the sum of the first integer and the fourth integer in terms of x.

Write the algebraic expression described. Simplify if possible. -Two numbers have a sum of 60. If one number is q, express the other number in terms of q.

Solve the equation. - $0.4 x - 0.6 x - 5 = 3$

Solve the equation. - $3 n = 5 ( 5 n + 8 )$

Solve the equation. - $- 10.4 z + 1.6 = - 42.9 - 1.5 z$

Write the algebraic expression described. Simplify if possible. -The sum of the angles of a triangle is $180 ^ { \circ }$ . If one angle of a triangle measures $x ^ { \circ }$ and a second angle measures $( 9 x + 18 ) ^ { \circ }$ , express the measure of the third angle in terms of $x$ .

Solve the equation. - $\frac { 1 } { 4 } ( x + 12 ) + \frac { 1 } { 6 } ( x + 6 ) = x + 8$

Write the algebraic expression described. Simplify if possible. -A 21-centimeter piece of rope is cut into two pieces. If one piece is z centimeters long, express the other length as an algebraic expression in z.

Solve the equation. - $( y - 8 ) - ( y + 2 ) = 5 y$

Write the algebraic expression described. Simplify if possible. -During a walk-a-thon, Rosilyn walked 18 fewer laps than June walked. If June walked b laps, how many laps did Rosilyn walk?

Quiz 2: Equations, Inequalities, and Problem Solving

Solve the equation. - 15(x+6) =17(x+8) \frac { 1 } { 5 } ( x + 6 ) = \frac { 1 } { 7 } ( x + 8 ) 51​(x+6) =71​(x+8)

Write the algebraic expression described. Simplify if possible. -In the race for Student Body President, Jose received 157 more votes than Angela. If Angela received x votes, how many votes did Jose receive?

Solve the equation. - 7x−(3x−1) =27 x - ( 3 x - 1 ) = 27x−(3x−1) =2

Solve. -A pharmacist is asked to give a customer 7.57.57.5 milliliters of an antibiotic over a period of 8 hours. If the antibiotic is to be given every 4 hours starting immediately, how much antibiotic should be given in each dose?

Solve the equation. - 13(5x−7) =3x−513 ( 5 x - 7 ) = 3 x - 513(5x−7) =3x−5