Equations and Inequalities

Erin weighs 135 pounds and is gaining "1" /"2" pound each week. Miranda weighs 143 pounds and is losing "1" /"4" pound each week. Which of the following equations could be used to determine x, the number of weeks that it will take until the two girls weigh the same amount?

• 135 + "1" /"2" x = 143 + "1" /"4" x

• 135 + "1" /"2" x = 143 - "1" /"4" x

• 135x + "1" /"2" = 143x + "1" /"4"

• 135 - "1" /"2" x = 143 + "1" /"4" x

A video game store allows customers to rent games for $4.75 each. Customers can also buy a membership for $54 annually, and video games would only cost $2.50 each. Write and solve an equation to find the number of video games a customer would have to rent in a year in order for the two options to be equal. What is the solution to the problem

• x=32

• x=42

• x = 24

• not shown

• Equation: -4x + 6 = -2x – 2; Solution: x = 4

• Equation: 6x + 4 = -2x + 2; Solution: x = -"1" /"4"

• Equation: 6x – 4 = -2x – 2; Solution: x = -"3" /"2"

• Equation: 6x – 4 = -2x – 2; Solution: x = "1" /"4"

Keith is in a hot air balloon that is 200 feet above the ground and is ascending 1"1" /"2" feet per second. Erica is in a hot air balloon that is 548 feet above the ground and is descending 1"2" /"5" feet per second. After how many seconds will the hot air balloons be the same number of feet above the ground?

• A.52 seconds

• 120 seconds

• 75 seconds

• 3,480 seconds

Mike is driving a boat at 12 mph and is increasing his speed by 0.2 mph each second. Hank is driving a boat at 25 mph and is decreasing his speed by 0.7 mph each second. Which of the following equations could be used to determine x, the number of seconds it will take for the boats to be traveling the same speed?

• 12x + 0.2 = 25x – 0.7

• .12 – 0.2x = 25 + 0.7x

• 12.2x = -25.7x

• 12 + 0.2x = 25 – 0.7x

Solve for f:
f - 4 = 6f + 26

• f = -5

• f = 5

• f = 6

• f = -6

Solve for x:
5x - 14 = 8x + 4

• x = 6

• x = -6

• x = -18/13

• x = 10/3

Solve the equation:
7x - 4 = 3 + 8x

• x = 7

• x = -7

• x = 2/7

• x = 11

8 - 9t = 21t - 17

• t = 6/5

• t = 5/6

• t = 1

5 - 2t = 3t

• 1

• 5

• 3

• 2