6th Grade Math Textbook, Fundamentals

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2-5

Remember:To subtract an integer,

add the opposite, or additive inverse,

of the number being subtracted.

Key Concept

Addition Property of Equality

When you add the same number to

both sides of an equation, you get a

true statement.

If ab, then acbc.

subtraction equation

Think

Whenever you add a number to

one side of an equation, you

must add the same number to

the other side to keep the

equation in balance.

The new equation is equivalent

to the original equation.

Update your skills. See page 409 VI.

Solve Subtraction Equations

Objective To apply the Addition Property of Equality to solve algebraic subtraction

equations with integers • To write a related sentence to solve for the subtrahend

• To combine numerical terms to simplify subtraction equations with integers

Lowell Middle School held a vote on whether or not to
change the name of the school basketball team to the
Gold Stars. Forty-two students were absent at the time
of the vote. The 914 students present all voted “Yes.”
How many students are enrolled at Lowell Middle School?

To find the number of students enrolled, write and solve

a.

Let sthe number of students enrolled at

Lowell Middle School.

students students is equal to students

enrolled absent present

s  42  914

To solve a subtraction equation, use the.

Remember that addition is the inverse operation of subtraction.

Solve: s 42  914

s 42  42  914  42

s 956

Check: s 42  914

956 42 914 Substitute 956 for s.

914  914 Tr u e

So 956 is the solution of the subtraction equation s 42 914.

There are 956 students enrolled in Lowell Middle School.

When the number being subtracted is negative, follow

the rules for subtracting integers. Then use the

Subtraction Property of Equality.

Solve:m(8)  34

m 8  34

m 8  8  34  8 Use the Subtraction Property of Equality.

m 26

Check:m (8)  34

26  (8) 34 Substitute 26 for m.

26  8 34

34  34 Tr u e

?

?

Rewrite the equation by following

the rules for subtracting integers.

?

Add 42 to both sides

to isolate s.

Addition Property of Equality

subtraction equation