Practice Identity vs Equation in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

An identity is an equation that holds true for all possible values of the variable, such as $(a+b)^2 = a^2 + 2ab + b^2$ . A conditional equation is true only for specific values, like $x + 3 = 7$ (true only when $x = 4$ ).

$a + a = 2a$ is always true (identity). $x + 3 = 7$ is only true when $x = 4$ (equation).

Showing a random 20 of 50 problems.

Example 1

hard

Solve

mx+5=4x+5

for

m

so that all real

x

are solutions.

Example 2

medium

Solve

4x+2=2(2x+1)

and interpret the result.

Example 3

medium

a(b + c) = ab + ac

an identity?

Example 4

easy

2(x + 3) = 2x + 6

an identity or an equation with specific solutions?

Example 5

easy

Classify:

x+5=x+3

Example 6

medium

Decide if

\sin

-free statement

2(x+3)=2x+5

is an identity, conditional, or contradiction.

Example 7

medium

Find

a

and

b

a(x+1)+b(x-1)=4x+2

is an identity.

Example 8

medium

(x-1)^2=x^2-1

an identity? If not, find all

x

where it holds.

Example 9

medium

Find all

x

for which

\frac{x}{x}=1

Example 10

medium

For what value of

b

5x-b=5x-3

an identity?

Example 11

medium

For what

k

does

kx+6=2x+6

become an identity?

Example 12

medium

Classify:

\frac{x^2-9}{x-3}=x+3

Example 13

easy

Classify:

2x=10

Example 14

medium

Show that

a^2-b^2=(a-b)(a+b)

is an identity.

Example 15

medium

Solve

3(x+1)=3x+3

and classify the result.

Example 16

easy

Classify:

(a+b)^2=a^2+2ab+b^2

Example 17

easy

Classify:

x^2=4

Example 18

easy

Classify:

x-7=0

Example 19

medium

Classify

\sqrt{x^2}=x

Example 20

easy

(x+2)(x-2)=x^2-4

an identity?

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Related Concepts

Equations Algebraic Identities Solving Linear Equations