Solving Equations and Inequality Word Problems with Variables on Both Sides

8w - 8 = - 4x + 16

• 8
• 16
• 24
• 2

2x - 3 + 4x = 27

• 12
• 4
• 5
• 15

5x - 4 + 2x = 3

• 1
• 2
• 3
• 4

10x + 9 = 4x - 9

• 0
• 3
• -3
• -18

Tricia and Melanie are both saving money for their summer vacations. They both began saving at the same time. Tricia started with $10.25 and adds $5.15 to her savings every month. Melanie did not have a starting amount but adds $10.25 to her savings every month. Which equation could be used to determine how many months, m, it will take before Tricia and Melanie both have saved the same amount of money?

• 5.15m + 10.25 = 10.25m

• 10.25m + 5.15 = 10.25m

• 10.25m + 10.25 = 5.15m

• 10.25m – 5.15 = 10.25m

Jack and Tim are racing remote-controlled cars. Jack’s car travels 3.5 feet per second, while Tim’s car travels 5.25 feet per second. Because Jack’s car is slower, Tim gave Jack a 10-foot head start. Which inequality could be used to determine after how many seconds, s, Tim’s car will be ahead of Jack’s car?

• 3.5s > 5.25s + 10

• 3.5s + 10 > 5.25s

• 5.25s > 3.5s + 10

• 3.5s – 10 < 5.25s

Which problems situation can be represented by the inequality below?

25 + 12.50c ≥ 22.50c – 95

• Charles and Victor went to a comic store and purchased some comic books. Charles purchased c comic books for $12.50 each and then spent $25.00 on a comic book portfolio. Victor sold a vintage comic book to the store for $95.00 and then purchased c more comic books for $22.50 each. How many comic books, c, would each boy purchase if Charles’ total amount due is greater than or equal to Victor’s total?

• Charles and Victor went to a comic store and purchased some comic books. Charles purchased c comic books for $22.50 each and then spent $25.00 on a comic book portfolio. Victor sold a vintage comic book to the store for $95.00 and then purchased c more comic books for $12.50 each. How many comic books, c, would each boy purchase if Charles’ total amount due is greater than or equal to Victor’s total?

• Charles and Victor went to a comic store and purchased some comic books. Charles purchased c comic books for $12.50 each and then spent $25.00 on a comic book portfolio. Victor purchased a vintage comic book from the store for $95.00 and then purchased c more comic books for $22.50 each. How many comic books, c, would each boy purchase if Charles’ total amount due is greater than or equal to Victor’s total?

• Charles and Victor went to a comic store and purchased some comic books. Charles purchased c comic books for $22.50 each and then spent $25.00 on a comic book portfolio. Victor purchased a vintage comic book from the store for $95.00 and then purchased c more comic books for $12.50 each. How many comic books, c, would each boy purchase if Charles’ total amount due is greater than or equal to Victor’s total?

Roxy and Randy are selling pancake breakfast plates to raise money for a class trip. Roxy is selling plates for $5.00 and has already raised $175. Randy is selling plates for $3.50 and has already raised $250. Which equation can be used to find p, the number of plates that Roxy and Randy must sell so that the total amount raised is the same for both Roxy and Randy?

• 5p + 250 = 3.50p + 175

• 250p + 3.50 = 175p + 5

• 3.50p + 250 = 5p + 175

• All of the above

An equation is represented by the model.

What is the value of x that makes the equation true?

• x = 7.5

• x = 1.5

• x = -1/10

• x = 2/3

What equation is represented by the model?

• -6x + 8 = 4x - 7

• -6x - 8 = 4x - 7

• 6x + 8 = -4x + 7

• 6x - 8 = -4x + 7