Question

(x + 2/3x) - ⅓(x + 2/3x) = 10

Answer 1

Answer:

x=9

Step-by-step explanation:

Solve for x

(

x

+

2

3

x

)

−

1

3

(

x

+

2

3

x

)

=

10

Simplify

x

+

2

3

x

−

1

3

⋅

(

x

+

2

3

x

)

.

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Simplify each term.

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x

+

2

x

3

−

5

x

9

=

10

Find the common denominator.

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x

⋅

9

9

+

2

x

⋅

3

9

−

5

x

9

=

10

Combine fractions with similar denominators.

x

⋅

9

+

2

x

⋅

3

−

5

x

9

=

10

Subtract

5

x

from

x

⋅

9

.

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2

x

⋅

3

+

4

⋅

x

9

=

10

Multiply

3

by

2

.

6

x

+

4

⋅

x

9

=

10

Add

6

x

and

4

⋅

x

.

10

x

9

=

10

Multiply both sides of the equation by

9

10

.

9

10

⋅

10

x

9

=

9

10

⋅

10

Simplify both sides of the equation.

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Simplify

9

10

⋅

10

x

9

.

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x

=

9

10

⋅

10

Cancel the common factor of

10

.

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Cancel the common factor.

x

=

9

10

⋅

10

Rewrite the expression.

x

=

9

Answer 2

Answer:

x = 9

Step-by-step explanation:

Given

(x + $\frac{2}{3}$ x ) - $\frac{1}{3}$(x + $\frac{2}{3}$ x ) = 10 ← distribute parenthesis

x + $\frac{2}{3}$ x - $\frac{1}{3}$ x - $\frac{2}{9}$ x = 10

Multiply through by 9 ( the LCM of 3 and 9 ) to clear the fractions

9x + 6x - 3x - 2x = 90

10x = 90 ( divide both sides by 10 )

x = 9