Solve the equation x + 32 5 86.

Step 1: Decide what needs removed to get the variable x by itself. You need to remove the “+ 32.”

Step 2: Remove the “+ 32” by doing the opposite, or inverse, operation. In this case, to remove “+ 32” you need to subtract 32. When you subtract 32 from one side of the equation, you must also subtract it from the other side. Subtract 32 from each side of the equation.

x + 32 – 32 = 86 – 32

Step 3: Do the math.

x = 54

Test-Taking Hint

Inverse operations can be used to check the answers to computations. For example, use addition to check your subtraction.

TEST TIME: Show Your Work

YoMinh solved the equation f + 2 = ^–6 and got the answer f = ^–4.

Is YoMinh’s answer correct? If not, what is the correct answer?

You can check the solution by replacing the variables in an equation with the solution. If the equation is true, the solution is correct.

Solution: f + 2 = ^–6
^–4 + 2 = ^–6
^–2 = ^–6

YoMinh does not have the correct answer.

f + 2 = ^–6
f + 2 – 2 = ^–6 – 2

The correct answer is f = ^–8

Check the solution.

f + 2 = ^–6
^–8 + 2 = ^–6
^–6 = ^–6

Addition Word Problems

A florist pays $12 for a dozen roses, then adds her markup and sells them for $36. Write an algebraic equation and solve it to find the markup on a dozen roses.

Step 1: Write a sentence to show what the problem is saying.

dollars paid plus markup is selling dollars

Step 2: Choose a variable for the value you don’t know. Replace the words with numbers, operation symbols, and variables.

Let m = markup
12 + m = 36

Step 3: Decide what needs to be removed to get the variable m by itself. You need to remove the 12.

Step 4: Remove the 12, or “+ 12”” by doing the opposite, or inverse, operation. Subtract 12 from each side of the equation.

12 + m – 12 = 36 – 12

Step 5: Do the math.

m = 24

The markup on a dozen roses is $24.

Test-Taking Hint

Read problems carefully. Decide how you can use the information given to solve the problem.

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Addition Problems