IXL | Identify equivalent equations

Select all of the equations below that are equivalent to:

r − 70 = ^–85

Use properties of equality.

r − 70

^–5

r − 70

^–5

r − 70

^–5

r − 70

^–17

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question

Select all of the equations below that are equivalent to:

q + r = 5

Use properties of equality.

key idea

The Subtraction Property of Equality says that if you subtract the same number from both sides of an equation, then the two sides are still equal.

solution

Go through the answer choices one by one.

First, take

14 + q + r = 20

. Is it equivalent to

q + r = 5

14 + q + r

Subtract 14 from both sides

14 − 14 + q + r

20 − 14

Subtract 14 from both sides

Simplify

q + r

Simplify

No,

14 + q + r = 20

is not equivalent to

q + r = 5

.

Second, take

11 + q + r = 16

. Is it equivalent to

q + r = 5

11 + q + r

Subtract 11 from both sides

11 − 11 + q + r

16 − 11

Subtract 11 from both sides

Simplify

q + r

Simplify

Yes,

11 + q + r = 16

is equivalent to

q + r = 5

.

Third, take

5 + q + r = 9

. Is it equivalent to

q + r = 5

5 + q + r

Subtract 5 from both sides

5 − 5 + q + r

9 − 5

Subtract 5 from both sides

Simplify

q + r

Simplify

No,

5 + q + r = 9

is not equivalent to

q + r = 5

.

Fourth, take

q + r + 2 = 9

. Is it equivalent to

q + r = 5

q + r + 2

Subtract 2 from both sides

q + r + 2 − 2

9 − 2

Subtract 2 from both sides

Simplify

q + r

Simplify

No,

q + r + 2 = 9

is not equivalent to

q + r = 5

According to the Subtraction Property of Equality, this equation is equivalent to

q + r = 5

11 + q + r = 16

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M.5Properties of equality

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