IXL - Identify equivalent equations (Algebra 1 practice)

Select all of the equations below that are equivalent to:

9 = c − d

Use properties of equality.

(

−

)

(

−

)

^–54

^–6

(

−

)

^–36

(

−

)

^–4

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Learn with an example

question

Select all of the equations below that are equivalent to:

^–100 = x + 25

Use properties of equality.

^–3

x + 25

^–2

x + 25

^–19

x + 25

^–20

key idea

The Multiplication Property of Equality says that if you multiply both sides of an equation by the same number, then the two sides are still equal.

solution

Go through the answer choices one by one.

First,
take
^–3 =
x + 25
20
.
Is
it
equivalent
to
^–100 = x + 25
?

^–3

x + 25

Multiply both sides by 20

^–3 · 20

x + 25

Multiply both sides by 20

Simplify

^–60

x + 25

Simplify

No,
^–3 =
x + 25
20
is
not
equivalent
to
^–100 = x + 25
.

Second,
take
^–2 =
x + 25
25
.
Is
it
equivalent
to
^–100 = x + 25
?

^–2

x + 25

Multiply both sides by 25

^–2 · 25

x + 25

Multiply both sides by 25

Simplify

^–50

x + 25

Simplify

No,
^–2 =
x + 25
25
is
not
equivalent
to
^–100 = x + 25
.

Third,
take
^–19 =
x + 25
5
.
Is
it
equivalent
to
^–100 = x + 25
?

^–19

x + 25

Multiply both sides by 5

^–19 · 5

x + 25

Multiply both sides by 5

Simplify

^–95

x + 25

Simplify

No,
^–19 =
x + 25
5
is
not
equivalent
to
^–100 = x + 25
.

Fourth,
take
5 =
x + 25
^–20
.
Is
it
equivalent
to
^–100 = x + 25
?

x + 25

^–20

Multiply both sides by ^–20

5 · ^–20

x + 25

^–20

Multiply both sides by ^–20

Simplify

^–100

x + 25

Simplify

Yes,
5 =
x + 25
^–20
is
equivalent
to
^–100 = x + 25
.

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

^–100 = x + 25

x + 25

^–20

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C.4Properties of equality

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