Question 1

Solve. $5 + x = 9$

Accepted Answer

A)  45 
B)  -4 
C)  4 
D)  14 
E)  -5 
A)  45 
B)  -4 
C)  4 
D)  14 
E)  -5

Question 2

The equation has a letter other than x as a variable. Solve for the variable. $59 = \frac { 9 } { 5 } C + 32$

Accepted Answer

A)  C = 25 
B)  C = 15 
C)  C = 12 
D)  C = 17 
E)  C = 10 
A)  C = 25 
B)  C = 15 
C)  C = 12 
D)  C = 17 
E)  C = 10

Question 3

Use two calculators tables to solve the equation. $$- 1 ( x - 6 ) = 3 ( x - 5 )$$

Accepted Answer

A)  x = 6.25 
B)  x = -5.25 
C)  x = 5.25 
D)  x = 4.25 
E)  x = -4.25 
A)  x = 6.25 
B)  x = -5.25 
C)  x = 5.25 
D)  x = 4.25 
E)  x = -4.25

Question 4

Check the "solution" of the equation by substituting the number into the equation. Note any wrong "solution." Explain how to solve the equation correctly. $$3 n = 9 , n = 2$$

Accepted Answer

A)  Multiply by 3. The correct solution is n = 3. 
B)  Divide by 3. The correct solution is n = 3. 
C)  The solution is correct. 
D)  Divide by 3. The correct solution is n = 5. 
E)  Multiply by 3. The correct solution is n = 5. 
A)  Multiply by 3. The correct solution is n = 3. 
B)  Divide by 3. The correct solution is n = 3. 
C)  The solution is correct. 
D)  Divide by 3. The correct solution is n = 5. 
E)  Multiply by 3. The correct solution is n = 5.

Question 5

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

Accepted Answer

A)  $x = - 4 \frac { 2 } { 3 }$ 
B)  $x = 4 \frac { 2 } { 3 }$ 
C)  $x = 2 \frac { 1 } { 3 }$ 
D)  $x = - 2 \frac { 1 } { 3 }$ 
E)  $x = 3 \frac { 2 } { 3 }$ 
A)  $x = - 4 \frac { 2 } { 3 }$ 
B)  $x = 4 \frac { 2 } { 3 }$ 
C)  $x = 2 \frac { 1 } { 3 }$ 
D)  $x = - 2 \frac { 1 } { 3 }$ 
E)  $x = 3 \frac { 2 } { 3 }$

Question 6

Use a calculator graph to solve the equation. $$2 ( x - 1 ) = 10 x - 2$$

Accepted Answer

A)  x = -1 
B)  x = 10 
C)  x = 0 
D)  x = 8 
E)  x = -2 
A)  x = -1 
B)  x = 10 
C)  x = 0 
D)  x = 8 
E)  x = -2

Question 7

Complete the table for j, k, m, and n. Then chose the correct answer. $$\begin{array} { l l l l l l l } 
x & 0 & j & k & m & n & 1 \
y = 5 - 5 x & 5 & 4 & 3 & 2 & 1 & 0
\end{array}$$

Accepted Answer

A)  j = $\frac { 1 } { 4 }$ 
B)  j = $\frac { 4 } { 5 }$ 
C)  n = $\frac { 1 } { 5 }$ 
D)  n = $\frac { 1 } { 4 }$ 
E)  n = $\frac { 4 } { 5 }$ 
A)  j = $\frac { 1 } { 4 }$ 
B)  j = $\frac { 4 } { 5 }$ 
C)  n = $\frac { 1 } { 5 }$ 
D)  n = $\frac { 1 } { 4 }$ 
E)  n = $\frac { 4 } { 5 }$

Question 8

Solve. $$2 x + 6 = 70 - 6 x$$

Accepted Answer

A)  x = 1 
B)  x = 8 
C)  x = -56 
D)  x = 64 
E)  x = -68 
A)  x = 1 
B)  x = 8 
C)  x = -56 
D)  x = 64 
E)  x = -68

Question 9

Solve. $3 x + 3 ( x - 3 ) = 9$

Accepted Answer

A)  x = 5 
B)  x = 12 
C)  x = 6 
D)  x = 3 
E)  x = -3 
A)  x = 5 
B)  x = 12 
C)  x = 6 
D)  x = 3 
E)  x = -3

Question 10

Solve the equation from the table. $$- 4 - 4 x = - 20$$ 
$\begin{array}{ cc}
 \text { x   } &   \text {   y=-4-4x} \
1& -8\
2& -12\
3&-16\
4&-20 \
\end{array}$

Accepted Answer

A)  $x = 2$ 
B)  $x = 0$ 
C)  $x = 4$ 
D)  $x = 5$ 
E)  $x = 7$ 
A)  $x = 2$ 
B)  $x = 0$ 
C)  $x = 4$ 
D)  $x = 5$ 
E)  $x = 7$

Question 11

Solve the equation from the table. $$\begin{array}{cc}
\underline { x } &\underline { y  = 8 - 2 x}\

1 & 6 \
2 & 4 \
3 & 2 \
4 & 0
\end{array}$$ $$8 - 2 x = 0$$

Accepted Answer

A)  x = 4 
B)  x = 1 
C)  x = 2 
D)  x = 3 
E)  x = 8 
A)  x = 4 
B)  x = 1 
C)  x = 2 
D)  x = 3 
E)  x = 8

Question 12

Write the equation as a sentence: $\frac { 3 } { 4 } x = 24$

Accepted Answer

A)  Three-fourths times 24 is a number. 
B)  Three-fourths of a number is 24. 
C)  Three-fourths of 24 is a number. 
D)  Three times a number less 4 is 24. 
E)  The quotient of $\frac { 3 } { 4 }$ and a number is 24. 
A)  Three-fourths times 24 is a number. 
B)  Three-fourths of a number is 24. 
C)  Three-fourths of 24 is a number. 
D)  Three times a number less 4 is 24. 
E)  The quotient of $\frac { 3 } { 4 }$ and a number is 24.

Question 13

Solve. $m - 9 = - 7$

Accepted Answer

A)  7 
B)  -2 
C)  16 
D)  2 
E)  9 
A)  7 
B)  -2 
C)  16 
D)  2 
E)  9

Question 14

Write the sentence as a two-variable equation containing parentheses. Describe your variables so y depends on x. The total cost of an air-compressor rental is $47 for the first day plus $33 for each additional day.

Accepted Answer

A)  y = 47 for x = 1; y = 47 + (33 - 1)x for x > 1 
B)  y = 47 for x = 1; y = 47 + 33(x + 1) for x > 1 
C)  y = 47 for x = 1; y = 47 + 33(x - 1) for x > 1 
D)  y = 33 for x = 1; y = 33 + 47(x - 1) for x > 1 
E)  y = 47 for x = 1; y = 47 + 33x for x > 1 
A)  y = 47 for x = 1; y = 47 + (33 - 1)x for x > 1 
B)  y = 47 for x = 1; y = 47 + 33(x + 1) for x > 1 
C)  y = 47 for x = 1; y = 47 + 33(x - 1) for x > 1 
D)  y = 33 for x = 1; y = 33 + 47(x - 1) for x > 1 
E)  y = 47 for x = 1; y = 47 + 33x for x > 1

Question 15

Solve the equation. $$5 ( x + 5 ) = 8$$

Accepted Answer

A)  $x = - 3.2$ 
B)  $x = 3.2$ 
C)  $x = 3.4$ 
D)  $x = - 3.4$ 
E)  $x = 3.8$ 
A)  $x = - 3.2$ 
B)  $x = 3.2$ 
C)  $x = 3.4$ 
D)  $x = - 3.4$ 
E)  $x = 3.8$

Question 16

Solve. $$5 - 6 x = 7 - 4 x$$

Accepted Answer

A)  x = -1 
B)  x = -8 
C)  x = 2 
D)  x = 1 
E)  x = 10 
A)  x = -1 
B)  x = -8 
C)  x = 2 
D)  x = 1 
E)  x = 10

Question 17

Solve the equation from the table. $$- 12 - 3 x = - 21$$ 
$\begin{array}{ cc}
 \text { x   } &   \text {   y=-12-3 x} \
1& -15\
2& -18\
3& -21\
4&-24 \
\end{array}$

Accepted Answer

A)  $x = - 5$ 
B)  $x = - 14$ 
C)  $x = - 10$ 
D)  $x = - 8$ 
E)  $x = 3$ 
A)  $x = - 5$ 
B)  $x = - 14$ 
C)  $x = - 10$ 
D)  $x = - 8$ 
E)  $x = 3$

Question 18

Solve. $$\frac { 5 } { 6 } x - 1 = \frac { 1 } { 6 } x + 15$$

Accepted Answer

A)  x = 90 
B)  x = 23 
C)  x = 16 
D)  x = 26 
E)  x = 24 
A)  x = 90 
B)  x = 23 
C)  x = 16 
D)  x = 26 
E)  x = 24

Question 19

State the inverse operation needed to solve the equation. Solve the equation. $- \frac { x } { 11 } = 5$

Accepted Answer

A)  Multiply by -11; x = -55 
B)  Multiply by 11; x = -55 
C)  Multiply by -11; x = 55 
D)  Divide by 11; x = 55 
E)  Divide by -11; x = 55 
A)  Multiply by -11; x = -55 
B)  Multiply by 11; x = -55 
C)  Multiply by -11; x = 55 
D)  Divide by 11; x = 55 
E)  Divide by -11; x = 55

Question 20

The area of a triangle is $A = \frac { 1 } { 2 } b h$ . If A = 7 and h = 2, solve for b.

Accepted Answer

A)  b = 7 
B)  b = 8 
C)  b = 14 
D)  b = 10 
E)  b = 3.5 
A)  b = 7 
B)  b = 8 
C)  b = 14 
D)  b = 10 
E)  b = 3.5

Solve. $5 + x = 9$

The equation has a letter other than x as a variable. Solve for the variable. $59 = \frac { 9 } { 5 } C + 32$

Use two calculators tables to solve the equation. $- 1 ( x - 6 ) = 3 ( x - 5 )$

Check the "solution" of the equation by substituting the number into the equation. Note any wrong "solution." Explain how to solve the equation correctly. $3 n = 9 , n = 2$

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

Use a calculator graph to solve the equation. $2 ( x - 1 ) = 10 x - 2$

Complete the table for j, k, m, and n. Then chose the correct answer. x 0 j k m n 1 y=5-5x 5 4 3 2 1 0

Solve. $2 x + 6 = 70 - 6 x$

Solve. $3 x + 3 ( x - 3 ) = 9$

Solve the equation from the table. $- 4 - 4 x = - 20$ x y=-4-4x 1 -8 2 -12 3 -16 4 -20

Solve the equation from the table. 1 6 2 4 3 2 4 0 $8 - 2 x = 0$

Write the equation as a sentence: $\frac { 3 } { 4 } x = 24$

Solve. $m - 9 = - 7$

Write the sentence as a two-variable equation containing parentheses. Describe your variables so y depends on x. The total cost of an air-compressor rental is $47 for the first day plus $33 for each additional day.

Solve the equation. $5 ( x + 5 ) = 8$

Solve. $5 - 6 x = 7 - 4 x$

Solve the equation from the table. $- 12 - 3 x = - 21$ x y=-12-3 x 1 -15 2 -18 3 -21 4 -24

Solve. $\frac { 5 } { 6 } x - 1 = \frac { 1 } { 6 } x + 15$

State the inverse operation needed to solve the equation. Solve the equation. $- \frac { x } { 11 } = 5$

The area of a triangle is $A = \frac { 1 } { 2 } b h$ . If A = 7 and h = 2, solve for b.

Algebraic Representations

Operations With Real Numbers

Ratios, Rates, and Proportional Reasoning

Formulas, Functions, Linear Equations, and Inequalities in Two Variables

Systems of Equations

Polynomial Expressions

Squares and Square Roots

Rational Expressions

Filters

Exam 3: Solving Equations

Solve. 5+x=95 + x = 95+x=9

The equation has a letter other than x as a variable. Solve for the variable. 59=95C+3259 = \frac { 9 } { 5 } C + 3259=59​C+32

Use two calculators tables to solve the equation. −1(x−6)=3(x−5)- 1 ( x - 6 ) = 3 ( x - 5 )−1(x−6)=3(x−5)

Check the "solution" of the equation by substituting the number into the equation. Note any wrong "solution." Explain how to solve the equation correctly. 3n=9,n=23 n = 9 , n = 23n=9,n=2

Solve the equation. 3(3−x)=−53 ( 3 - x ) = - 53(3−x)=−5

Use a calculator graph to solve the equation. 2(x−1)=10x−22 ( x - 1 ) = 10 x - 22(x−1)=10x−2

Complete the table for j, k, m, and n. Then chose the correct answer. x 0 j k m n 1 y=5-5x 5 4 3 2 1 0

Solve. 2x+6=70−6x2 x + 6 = 70 - 6 x2x+6=70−6x

Solve. 3x+3(x−3)=93 x + 3 ( x - 3 ) = 93x+3(x−3)=9

Solve the equation from the table. −4−4x=−20- 4 - 4 x = - 20−4−4x=−20 x y=-4-4x 1 -8 2 -12 3 -16 4 -20

Solve the equation from the table. 1 6 2 4 3 2 4 0 8−2x=08 - 2 x = 08−2x=0

Write the equation as a sentence: 34x=24\frac { 3 } { 4 } x = 2443​x=24

Solve. m−9=−7m - 9 = - 7m−9=−7

Write the sentence as a two-variable equation containing parentheses. Describe your variables so y depends on x. The total cost of an air-compressor rental is $47 for the first day plus $33 for each additional day.

Solve the equation. 5(x+5)=85 ( x + 5 ) = 85(x+5)=8

Solve. 5−6x=7−4x5 - 6 x = 7 - 4 x5−6x=7−4x

Solve the equation from the table. −12−3x=−21- 12 - 3 x = - 21−12−3x=−21 x y=-12-3 x 1 -15 2 -18 3 -21 4 -24

Solve. 56x−1=16x+15\frac { 5 } { 6 } x - 1 = \frac { 1 } { 6 } x + 1565​x−1=61​x+15

State the inverse operation needed to solve the equation. Solve the equation. −x11=5- \frac { x } { 11 } = 5−11x​=5

The area of a triangle is A=12bhA = \frac { 1 } { 2 } b hA=21​bh . If A = 7 and h = 2, solve for b.

Algebraic Representations

Operations With Real Numbers

Ratios, Rates, and Proportional Reasoning

Formulas, Functions, Linear Equations, and Inequalities in Two Variables

Systems of Equations

Polynomial Expressions

Squares and Square Roots

Rational Expressions

Filters

Solve. $5 + x = 9$

The equation has a letter other than x as a variable. Solve for the variable. $59 = \frac { 9 } { 5 } C + 32$

Use two calculators tables to solve the equation. $- 1 ( x - 6 ) = 3 ( x - 5 )$

Check the "solution" of the equation by substituting the number into the equation. Note any wrong "solution." Explain how to solve the equation correctly. $3 n = 9 , n = 2$

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

Use a calculator graph to solve the equation. $2 ( x - 1 ) = 10 x - 2$

Solve. $2 x + 6 = 70 - 6 x$

Solve. $3 x + 3 ( x - 3 ) = 9$

Solve the equation from the table. $- 4 - 4 x = - 20$ x y=-4-4x 1 -8 2 -12 3 -16 4 -20

Solve the equation from the table. 1 6 2 4 3 2 4 0 $8 - 2 x = 0$

Write the equation as a sentence: $\frac { 3 } { 4 } x = 24$

Solve. $m - 9 = - 7$

Solve the equation. $5 ( x + 5 ) = 8$

Solve. $5 - 6 x = 7 - 4 x$

Solve the equation from the table. $- 12 - 3 x = - 21$ x y=-12-3 x 1 -15 2 -18 3 -21 4 -24

Solve. $\frac { 5 } { 6 } x - 1 = \frac { 1 } { 6 } x + 15$

State the inverse operation needed to solve the equation. Solve the equation. $- \frac { x } { 11 } = 5$

The area of a triangle is $A = \frac { 1 } { 2 } b h$ . If A = 7 and h = 2, solve for b.