Equations and Inequalities

What value of x satisfies the equation -2(10 + x) = 4x + 12 + 2x?

• 12

• 4

• 8

• -4

Charlotte wants to solve the equation 6(2x + 1) = 4x – 5. Which step would be an appropriate first step for Charlotte to take to solve for x?

• subtract 1 from both sides to combine like terms

• distribute the 6 to eliminate the parentheses

• add 4x to both sides to isolate the variable

• combine 4x and -5 to simplify the problem

Tags

CCSS.HSA.REI.A.1

Use the inequality to answer the following question. 3(x – 4) ≤ 8x + 13. Which of the following inequalities could be the result of the first step in solving the inequality for x?

• x – 4 ≤ (8/3)x + 13

• x – 4 ≤ 8x + 10

• 3x – 4 ≤ 8x + 13

• 3x – 12 ≤ 8x + 13

Tags

CCSS.HSA.REI.A.1

Lloyd solves the equation 24x + 18(x – 2) = 216 for x. Some of his steps are shown. Step 1: 24x + 18(x – 2) = 216 Step 2: 24x + 18x – 36 = 216 Step 3: 42x – 36 = 216 Step 4: 42x = 252 Which of the following statements BEST describes what Lloyd did to get from Step 3 to Step 4?

• combined liked terms

• used the distributive property

• used the addition property of equality

• used the multiplicative inverse property

Tags

CCSS.8.EE.C.7B

Use the graph of the compound inequality to answer the following question.

Which of the following inequalities has the solution set that is shown in the graph?

• -2 ≤ x ≤ 3

• -2 < x < 3

• -2 ≤ x < 3

• -2 < x ≤ 3

What error has the student made? A possible error has been made in the following expression as shown in the student work.

• Student did not combine like terms correctly

• Student did not distribute the negative sign correctly

• Student did not apply the integer rules correctly

• Student did not make an error

Tags

CCSS.HSA.APR.A.1

Simplify the given expression above. What is the correct answer?

• 3x² - 11x - 3

• 3x² + 3x - 7

• 9x² + 3x - 3

• 9x² + 11x - 7

Tags

CCSS.HSA.APR.A.1

What error did Fred make between Step 1 and Step 2? Explain your reasoning.

• Fred did not combine like terms correctly

• Fred did not distribute the negative sign correctly

• Fred did not divide correctly

• Fred did not make an error

Tags

CCSS.HSA.REI.A.1

Solve the following equation $\frac{1}{2}w + 7 = 2w - 14 + 12$.

• w = 14

• w = 6

• w = 7

• w = -1

Solve the following inequality -2x + 7 ≤ 5. What is the correct solution?

• x ≤ 1

• x > 1

• x ≥ 1

• x ≤ -1

Tags

CCSS.7.EE.B.4B