Equations Inequalities

Using the "opposite operation" to "undo" and isolate the variable when solving an equation is more commonly called...

• Inverse operations

• math

• variable

• PEMDAS

A stadium has a total of  18,000 seats.  Of these, 7,500 are field seats, and the rest are grandstand seats.  Write an equation that could be used to find the number of grandstand seats s. 

• 18,000 + 7,500 = s

• s + 7,500 = 18,000

• 7,500 - s = 18,000

• 7,500 - 18,000 = s

17 = x + 3

• x = 20

• x = 14

• x = 13

• x = 19

x - 32 = 49

• x = 17

• x = 71

• x = 81

• x = 49

From the problem below determine the keyword that determines the expression for Get Clean: The cost to rent a rug cleaner for a day is $25 plus $15 per hour at Rugs Galore. At Get Clean the rug cleaner costs $45 plus $7 per hour. Write an inequality that can be used to show how many hours you need to rent the rug cleaner so that Get Clean’s charges will be less than Rugs Galore’s charges.

• y = 15x + 25

• y = 25x + 15

• y = 45x + 7

• y = 7x + 45

Which equation represents the line that passes through (-2, 7) and is perpendicular to the x-axis? 

• y = 7

• x = 7

• y = -2

• x = -2

From the problem below determine the keyword that determines the expression for Get Clean: The cost to rent a rug cleaner for a day is $25 plus $15 per hour at Rugs Galore. At Get Clean the rug cleaner costs $45 plus $7 per hour. Write an inequality that can be used to show how many hours you need to rent the rug cleaner so that Get Clean’s charges will be less than Rugs Galore’s charges.

• y = 15x + 25

• y = 25x + 15

• y = 45x + 7

• y = 7x + 45

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

x - 62 = 123
How should you show your work to isolate the variable and solve the equation?

• Add 62 to each side. 

• Subtract 62 from each side.

• Multiply each side by 62.

• Add 123 to each side.

Solve for x:

• x = 20

• x = 7

• x = 10

• x = 3