Question 1

Use a property of equality to solve the equation. Then check the result. $$y + 18 = 24$$ y = __________

Accepted Answer

6

Question 2

Use the division or the multiplication property of equality to solve the equation. $\frac { 12 } { 3 } = 6 x$
A)x = 6
B) $x = \frac { 1 } { 6 }$
C) $x = \frac { 2 } { 3 }$
D)x = 3

Accepted Answer

Applying the division property of equality, we get:
\begin{align*}
\frac{12}{3} &= 6x \
4 &= 6x \
\frac{4}{6} &= x \
\frac{2}{3} &= x
\end{align*} 
Therefore, the solution is x = 2/3, which corresponds to choice (C).

Question 3

Use a property of equality to solve the equation. Then check the result. $$a - 7 = 66$$ a = __________

Accepted Answer

73

Question 4

Tell whether the given number is a solution of the equation. $$8 k + 9 = 9 k - 1 ; k = 8$$
A)unqualified solution
B)removed solution
C)solution
D)not a solution
E)none of these

Accepted Answer

Substituting $k = 8$ into the equation $8k + 9 = 9k - 1$, we get $8(8) + 9 = 9(8) - 1$, which simplifies to $64 + 9 = 72 - 1$. This further simplifies to $73 \neq 71$, indicating that $k = 8$ does not satisfy the equation.

Question 5

Use the division or the multiplication property of equality to solve $\frac { v } { 6 } = 4$ . What is the result?
A)24
B)25
C)0.67
D)1.50
E)2.50

Accepted Answer

Using the multiplication property of equality, we can multiply both sides of the equation by 6 to isolate the variable v.

\begin{align*}
\frac{v}{6}&=4 \
v &= 4 	imes 6 \
v &= 24
\end{align*}

Therefore, the solution is v = 24, which corresponds to choice letter A.

Question 6

Use the division or the multiplication property of equality to solve $13 = \frac { y } { 8 }$ . What is the result?
A)1
B)208
C)104
D)0.13
E)103

Accepted Answer

To solve for y, we can use the multiplication property of equality and multiply both sides by 8.

\begin{align*}
13 &= \frac{y}{8} \
13 \cdot 8 &= \frac{y}{8} \cdot 8 \
104 &= y \
\end{align*}

Therefore, the solution is y = 104, which corresponds to option C.

Question 7

Use the division or the multiplication property of equality to solve $4 = \frac { v } { 8 }$ . What is the result? v = __________

Accepted Answer

The answer of Use the division or the multiplication property...

Question 8

Solve the equation. 9( z + 2)= 36
A)z = 1
B)z = 13
C)z = 6
D)z = 2
E)z = 9

Accepted Answer

To solve the equation, we need to isolate the variable z.

First, distribute the 9:

9z + 18 = 36

Then, subtract 18 from both sides:

9z = 18

Finally, divide both sides by 9:

z = 2

Therefore, the solution is z = 2, which corresponds to choice D.

Question 9

Solve the equation. $$9 y - 30 + 15 y - 9 y + 45 = 120$$
A)y = 12
B)y = -7
C)y = 3
D)y = 7
E)y = 8

Accepted Answer

The answer of Solve the equation. \[9 y - 30...

Question 10

Solve the equation. 6 x + 3 = 33
A)x = 8
B)x = 5
C)x = 4
D)x = 9
E)none of these

Accepted Answer

To solve for x, we need to isolate it on one side of the equation. We can do this by first subtracting 3 from both sides:

6x + 3 - 3 = 33 - 3 
6x = 30

Then, we can solve for x by dividing both sides by 6:

6x/6 = 30/6 
x = 5

Therefore, the answer is choice B.

Question 11

Solve the equation. 6.5 = -10 t + 9
A)t = 2.25
B)t = 0.25
C)t = 0.250
D)t = 6.25
E)none of these

Accepted Answer

To solve the equation 6.5 = -10t + 9, subtract 9 from both sides to get -2.5 = -10t. Then, divide both sides by -10 to find t = 0.25.

Question 12

Use the division or the multiplication property of equality to solve $3 x = 195$ . What is the result?
A)64
B)65
C)585
D)586
E)584

Accepted Answer

To solve for $x$, divide both sides of the equation by 3: $x = 195 / 3 = 65$.

Question 13

Solve the equation. 45 = -2 - 13 y
A) $y = \frac { 47 } { 13 }$
B) $y = - \frac { 47 } { 13 }$
C) $y = - \frac { 43 } { 13 }$
D) $y = - \frac { 13 } { 47 }$
E) $y = \frac { 43 } { 13 }$

Accepted Answer

To solve the equation $45 = -2 - 13y$, add 2 to both sides to get $47 = -13y$. Then, divide both sides by -13 to isolate $y$, resulting in $y = -\frac{47}{13}$.

Question 14

Solve the equation. 5( t - 1)+ 2( t - 1)= -2( t - 2)+ 10( t + 2)
A)t = -37
B)t = -33
C)t = -31
D)t = -25
E)t = -28

Accepted Answer

Starting with the left side of the equation, we can distribute the coefficients of t:

5(t-1) + 2(t-1)

= 5t - 5 + 2t - 2

= 7t - 7

Now let's do the same for the right side:

-2(t-2) + 10(t+2)

= -2t + 4 + 10t + 20

= 8t + 24

Now the equation becomes:

7t - 7 = 8t + 24

Subtracting 7t from both sides:

-t - 7 = 24

Adding 7 to both sides:

-t = 31

Multiplying by -1:

t = -31

Therefore, the answer is C.

Question 15

Use a property of equality to solve the equation. Then check the result. $$4 = m - 21$$ m = __________

Accepted Answer

The answer of Use a property of equality to solve...

Question 16

Tell whether the given number is a solution of the equation. $$\frac { y } { 3 } = 5 ; y = 18$$
A)restricted solution
B)not a solution
C)solution
D)conflicting solution
E)none of these

Accepted Answer

When substituting $ y = 18 $ into the equation $\frac{y}{3} = 5$, it results in $\frac{18}{3} = 6$, which does not equal 5. Therefore, $ y = 18 $ is not a solution.

Question 17

Use the division or the multiplication property of equality to solve $6 x = 432$ . What is the result? x = __________

Accepted Answer

The answer of Use the division or the multiplication property...

Question 18

Tell whether the number is a solution of the equation. $$\frac { 2 + x } { 8 } - x = \frac { 1 } { 4 } ; x = 0$$
A)non-quantified solution
B)unequal solution
C)not a solution
D)solution
E)none of these

Accepted Answer

Plugging in $x=0$, we get $\frac{2}{8}-0=\frac{1}{4}$. Simplifying, we get $\frac{1}{4}=\frac{1}{4}$, which is true. Therefore, $x=0$ is a solution of the equation.

Question 19

Use a property of equality to solve the equation. Then check the result. $$f + 3.5 = 1.2$$ f = __________

Accepted Answer

The answer of Use a property of equality to solve...

Question 20

Use a property of equality to solve the equation. Then check the result. $$a + 7 = 0$$ a = __________

Accepted Answer

The answer of Use a property of equality to solve...

Quiz 2: Equations, Inequalities, and Problem Solving

Use a property of equality to solve the equation. Then check the result. $y + 18 = 24$ y = __________

Use the division or the multiplication property of equality to solve the equation. $\frac { 12 } { 3 } = 6 x$

Use a property of equality to solve the equation. Then check the result. $a - 7 = 66$ a = __________

Tell whether the given number is a solution of the equation. $8 k + 9 = 9 k - 1 ; k = 8$

Use the division or the multiplication property of equality to solve $\frac { v } { 6 } = 4$ . What is the result?

Use the division or the multiplication property of equality to solve $13 = \frac { y } { 8 }$ . What is the result?

Use the division or the multiplication property of equality to solve $4 = \frac { v } { 8 }$ . What is the result? v = __________

Solve the equation. 9( z + 2) = 36

Solve the equation. $9 y - 30 + 15 y - 9 y + 45 = 120$

Solve the equation. 6 x + 3 = 33

Solve the equation. 6.5 = -10 t + 9

Use the division or the multiplication property of equality to solve $3 x = 195$ . What is the result?

Solve the equation. 45 = -2 - 13 y

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

Use a property of equality to solve the equation. Then check the result. $4 = m - 21$ m = __________

Tell whether the given number is a solution of the equation. $\frac { y } { 3 } = 5 ; y = 18$

Use the division or the multiplication property of equality to solve $6 x = 432$ . What is the result? x = __________

Tell whether the number is a solution of the equation. $\frac { 2 + x } { 8 } - x = \frac { 1 } { 4 } ; x = 0$

Use a property of equality to solve the equation. Then check the result. $f + 3.5 = 1.2$ f = __________

Use a property of equality to solve the equation. Then check the result. $a + 7 = 0$ a = __________

Quiz 2: Equations, Inequalities, and Problem Solving

Use a property of equality to solve the equation. Then check the result. y+18=24y + 18 = 24y+18=24 y = __________

Use the division or the multiplication property of equality to solve the equation. 123=6x\frac { 12 } { 3 } = 6 x312​=6x

Use a property of equality to solve the equation. Then check the result. a−7=66a - 7 = 66a−7=66 a = __________

Tell whether the given number is a solution of the equation. 8k+9=9k−1;k=88 k + 9 = 9 k - 1 ; k = 88k+9=9k−1;k=8

Use the division or the multiplication property of equality to solve v6=4\frac { v } { 6 } = 46v​=4 . What is the result?

Use the division or the multiplication property of equality to solve 13=y813 = \frac { y } { 8 }13=8y​ . What is the result?

Use the division or the multiplication property of equality to solve 4=v84 = \frac { v } { 8 }4=8v​ . What is the result? v = __________

Solve the equation. 9( z + 2) = 36

Solve the equation. 9y−30+15y−9y+45=1209 y - 30 + 15 y - 9 y + 45 = 1209y−30+15y−9y+45=120

Solve the equation. 6 x + 3 = 33

Solve the equation. 6.5 = -10 t + 9

Use the division or the multiplication property of equality to solve 3x=1953 x = 1953x=195 . What is the result?

Solve the equation. 45 = -2 - 13 y

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

Use a property of equality to solve the equation. Then check the result. 4=m−214 = m - 214=m−21 m = __________

Tell whether the given number is a solution of the equation. y3=5;y=18\frac { y } { 3 } = 5 ; y = 183y​=5;y=18

Use the division or the multiplication property of equality to solve 6x=4326 x = 4326x=432 . What is the result? x = __________

Tell whether the number is a solution of the equation. 2+x8−x=14;x=0\frac { 2 + x } { 8 } - x = \frac { 1 } { 4 } ; x = 082+x​−x=41​;x=0

Use a property of equality to solve the equation. Then check the result. f+3.5=1.2f + 3.5 = 1.2f+3.5=1.2 f = __________

Use a property of equality to solve the equation. Then check the result. a+7=0a + 7 = 0a+7=0 a = __________

Use a property of equality to solve the equation. Then check the result. $y + 18 = 24$ y = __________

Use the division or the multiplication property of equality to solve the equation. $\frac { 12 } { 3 } = 6 x$

Use a property of equality to solve the equation. Then check the result. $a - 7 = 66$ a = __________

Tell whether the given number is a solution of the equation. $8 k + 9 = 9 k - 1 ; k = 8$

Use the division or the multiplication property of equality to solve $\frac { v } { 6 } = 4$ . What is the result?

Use the division or the multiplication property of equality to solve $13 = \frac { y } { 8 }$ . What is the result?

Use the division or the multiplication property of equality to solve $4 = \frac { v } { 8 }$ . What is the result? v = __________

Solve the equation. $9 y - 30 + 15 y - 9 y + 45 = 120$

Use the division or the multiplication property of equality to solve $3 x = 195$ . What is the result?

Use a property of equality to solve the equation. Then check the result. $4 = m - 21$ m = __________

Tell whether the given number is a solution of the equation. $\frac { y } { 3 } = 5 ; y = 18$

Use the division or the multiplication property of equality to solve $6 x = 432$ . What is the result? x = __________

Tell whether the number is a solution of the equation. $\frac { 2 + x } { 8 } - x = \frac { 1 } { 4 } ; x = 0$

Use a property of equality to solve the equation. Then check the result. $f + 3.5 = 1.2$ f = __________

Use a property of equality to solve the equation. Then check the result. $a + 7 = 0$ a = __________