Addition and subtraction are inverse operations. You can sometimes use addition to get a variable by itself in a subtraction problem.

Solve the equation y – 2.5 = 6.3. Check the solution.

Step 1: Decide what needs to be removed to get the variable y by itself. You need to remove the “– 2.5.”

Step 2: Remove the “– 2.5” by doing the opposite, or inverse, operation. Add 2.5 to each side of the equation.

y – 2.5 + 2.5 = 6.3 + 2.5

Step 3: Do the math.

y = 8.8

Step 4: Check the solution. Replace the variable in the original problem with the solution.

8.8 – 2.5 = 6.3
6.3 = 6.3

TEST TIME: Explain Your Answer

Solve the equation 22 – d = 27 and explain how you found your solution.

Solution: Add the variable d to both sides of the equation first.

22 – d = 27
22 – d + d = 27 + d
22 = 27 + d

Then subtract 27 from each side to get d by itself.

22 = 27 + d
22 – 27 = 27 + d – 27
^–5 = d

This problem can also be solved by rewriting the subtraction equation as an addition equation. Change the subtraction sign to an addition sign and add the opposite.

22 – d = 27
22 + ^–d = 27

Subtract 22 from each side.

22 – 22 + ^–d = 27 – 22
^–d = 5

If ^–d = 5, then d = ^–5.

TEST TIME: Show Your Work

Gerald gave the cashier some money to pay for a chili dog, a bag of chips, and a pop. The cashier gave him back $4.75. Write and solve an algebraic equation to find the amount of money Gerald gave the cashier.

One way to write this equation is to use parentheses to add the cost of the items purchased first. You do not know the amount of money Gerald gave the cashier, so use a variable for that value.

Solution: amount paid minus amount spent equals change

p – ($2.50 + $1.25 + $1.50) = $4.75

Add inside the parentheses.

p – $5.25 = $4.75

Solve for p. p – $5.25 + $5.25 = $4.75 + $5.25

p = $10.00

Gerald gave the cashier $10.00.

Test-Taking Hint

Make notes in your test booklet to help you solve problems. For the problem on the previous page, you can make small marks next to the items on the menu that were purchased.

Calculators

Calculators are useful tools for solving and checking the solutions to math problems. It is still important to understand the problem and what to do with the numbers in the problem.

Use a calculator to check the solution to the problem on page 72.

One way: Begin with the solution. Start with $10.00 on the calculator. Subtract the price of each item Gerald purchased.

$10.00 – $2.50 – $1.25 – $1.50 = $4.75

Another way: Begin with the change. Add the price of each item Gerald purchased.

$4.75 + $2.50 + $1.25 + $1.50 = $10.00

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Subtraction Problems