M1 1.2 Practice

What is the solution to this inequality?

• x > -3

• x < -3

• x > 3

• x < 3

Solve for x.

• x ≥ -23/4

• x ≤ -23/4

• x ≥ 13/4

• x ≤ 13/4

What is the solution to this equation?

• x = -36

• x = -36/5

• x = -12

• x = -12/5

The steps in the solution to an equation are shown in the table.

Which of the following lists the properties in the correct order used in the steps of the solution?

• A, D, M, A

• A, M, D, A

• M, A, D, M

• M, D, A, M

Jacob is attempting to solve for x in the equation 7(x + 5) = 3(x - 8) using the steps shown. Steps shown: Step 1: 7(x + 5) = 3(x - 8) Step 2: 7x + 35 = 3x - 24 Step 3: 4x + 35 = -24 Step 4: 4x = 11 Step 5: x = 7 Which is the first incorrect step in Jacob’s solution?

• step 1

• step 4

• step 2

• step 3

Hector has $100 in savings and makes $7.50 per hour. Luis has $80 in savings and earns $12.75 for each hour worked. They work together for the same number of hours, and they save all of the money they earn. Luis wants to know how many hours he has to work to have the same amount of money in savings as Hector. Luis sets the expression representing his savings given his hours worked equal to the expression for Hector. Which equation should Luis use? Which is the logical first step to find the solution, and how can taking the step be justified?

• The equation is 12.75h + 100 = 7.50 + 80. The logical first step is to subtract 80 from both sides of the equation using the subtraction property of equality.

• The equation is 12.75h + 100 = 7.50h + 80. The logical first step is to subtract 7.50 from both sides using the subtraction property of equality.

• The equation is 7.50h + 100 = 12.75h + 80. The logical first step is to subtract 7.50h from both sides using the subtraction property of equality.

• The equation is 7.50h + 100 = 12.75h + 80. The logical first step is to add 80 to both sides of the equation using the additive property of equality.

What is the solution to the equation 2x - 45 = 7x - 9x - x?

• x = -45

• x = 45

• x = -9

• x = 9

Which is the first incorrect step in the solution shown below? Solve: 2 - 3(x - 1) = 13 Step 1: 2 - 3x - 1 = 13 Step 2: 1 - 3x - 1 = 13 Step 3: -3x = 12 Step 4: x = -4

• Step 2

• Step 1

• Step 3

• There are no errors.

Which graph shows the solution to the inequality below? 6 < -2x

• Graph B

• Graph A

• Graph C

• Graph D

In his solution, Harley applied three properties of equality: I. Addition property of equality II. Multiplication property of equality III. Distributive property In which order did Harley use the properties?

• III, I, II

• I, II, III

• II, I, III

• III, II, I