Absolute Value Equations and Inequalities

Solve the absolute value equation below. -64 = -2|4x + 8| Select the solution(s) to the absolute value equation.

• -18

• -17.5

• -10

• 6

Lisa and Joshua get a combined monthly allowance of $320. Lisa's monthly allowance is $20 more than half of Joshua's monthly allowance. If x represents Joshua's allowance, in dollars, which equation is true?

• x-(0.5x+20)=320

• x+(0.5x+20)=320

• x+320=0.5x+20

• x+(20x+0.5)=320

Lisa and Joshua get a combined monthly allowance of $320. Lisa's monthly allowance is $20 more than half of Joshua's monthly allowance. If x represents Joshua's allowance, in dollars, how much is his allowance?

• $200

• $ 300

• $320

• $350

The equation below represents the volume of a rectangular prism. V=lwh Which of the following equations is the volume equation rearranged to highlight length?

• l = wh / V

• l = V / wh

• l = V/w-h

• l = V - wh

Select the inequality below that represents the solution to 6x+1 ≤ 5x+2.

• x ≤ 1

• x ≥ -1

• 7x ≤ 7x

• x ≤ 3

Normal internal body temperature is defined as 98.6 degrees Fahrenheit; however there can be a 0.9 degree Fahrenheit variation among individuals that is still considered to be normal. Select the absolute value equation below that represents the situation.

• | 0.9+x | =98.6

• | 98.6-x | =0.9

• | x-0.9 | =98.6

• | 98.6-0.9 |=x

The equation for kinetic energy is represented by the equation below . Which of the following is the kinetic energy equation rearranged to highlight velocity, v?

• 
• 
• 
• 

Fill in the boxes with the appropriate numerical values to make this statement true. The solution to the compound inequality -50 < 7x+6 < -8 can be written in the form ⬜< x < ⬜

• 8 < x < -2

• 8 < x < 2

• -8 < x < 2

• -8 < x < -2

John and Farrah are writing an equation for the following real-world problem. A group of friends is planning a trip to the fair. The group pays $32 per ticket plus $20 to park their van. They each also decide to purchase a ride bracelet for $55. The group spends a total of $716. How many friends are in the group?

John writes the equation 32x+20+55=716 to represent the situation

Farrah writes the equation 32x+20+55x=716 to represent the situation

Harry writes the equation x(32+20+55)=716 to represent the situation.

Who wrote the correct equation ?

• John

• Farrah

• Harry

John and Farrah are writing an equation for the following real-world problem. A group of friends is planning a trip to the fair. The group pays $32 per ticket plus $20 to park their van. They each also decide to purchase a ride bracelet for $55. The group spends a total of $716. How many friends are in the group?

Based on the problem, what are the information to be considered in writing an equation?

• Each friend only pays for their own ticket and shares the other costs

• Each friend pays for their own ticket and ride bracelet and share the parking cost

• Each friend pays for their own ticket, ride bracelet, and parking