Solving Inequality and Equation Word Problems with the Variable on Both Sides

What is the first step to solve this equation:
-3x + 11 = 44

• Add 3 to both sides

• Subtract 11 from both sides

• Add 11 to both sides

• Divide 3 on both sides.

Look at the work. What was done incorrectly?

• Don't divide by 2 first

• Don't add 7 to both sides

• It's correct!

• They should have subtracted 7

Look at the work. What SHOULD have been the first step?

• It's correct!

• Subtract 1 on both sides

• Add 5 on both sides

• Divide by 3 on both sides

The 30 members of a choir are trying to raise at least $1,500 to cover travel costs to a singing camp. They have already raised $600. Which inequality could you solve to find the average amounts each member can raise that will at least meet the goal?

• 30x + 600 > 1,500

• 30x + 600 ≥ 1,500

• 30x + 600 < 1,500

• 30x + 600 < 1,500

Sam make $10.25 per hour working at Cheddars.  He plans to buy a laptop for $550.  Write and solve an inequality describing how many hours h Sam will have to work to be able to buy the laptop. (Round to the next higher hour)

• 10.25h < 550; less than 54 hours

• 10.25h > 550; greater than 54 hours

• 10.25h ≤ 550; at most 54 hours

• 10.25h ≥ 550; at least 54 hours

Last Friday Trevon had $29. Over the weekend he received some money for cleaning the attic. He now has $41. How much money did he receive?

• 29 - n = 41

• 29 - n = 40

• 29 + n = 41

• 29 + n = 40

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.

2x + 1 = 6

What would the first step be in solving this equation?

• Divide by 2

• Subtract 1

• Subtract 6

• Times 2

A taxi cab costs $1.75 and $0.75 for each additional mile. You have $20 to spend on you ride. Which inequality could be solved to find how many miles you can travel, if m is the number of additional miles?

• 1.75n + 0.75 ≥ 20

• 1.75n + 0.75 ≤ 20

• 0.75n + 1.75 ≥ 20

• 0.75n + 1.75 ≤ 20

Solve for b:
-11 + 3(b + 5) = 7

• b = 1

• b = -1

• b = 3

• b = -3