Algebra Examples

23 = \frac{7}{9} (6 x - 36) + 9

$23 = \frac{7}{9} (6 x - 36) + 9$

Step 1

Rewrite the equation as

\frac{7}{9} \cdot (6 x - 36) + 9 = 23

$\frac{7}{9} \cdot (6 x - 36) + 9 = 23$ .

\frac{7}{9} \cdot (6 x - 36) + 9 = 23

$\frac{7}{9} \cdot (6 x - 36) + 9 = 23$

Step 2

Simplify

\frac{7}{9} \cdot (6 x - 36) + 9

$\frac{7}{9} \cdot (6 x - 36) + 9$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

\frac{7}{9} (6 x) + \frac{7}{9} \cdot - 36 + 9 = 23

$\frac{7}{9} (6 x) + \frac{7}{9} \cdot - 36 + 9 = 23$

Step 2.1.2

Cancel the common factor of

3

$3$ .

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Step 2.1.2.1

Factor

3

$3$ out of

9

$9$ .

\frac{7}{3 (3)} (6 x) + \frac{7}{9} \cdot - 36 + 9 = 23

$\frac{7}{3 (3)} (6 x) + \frac{7}{9} \cdot - 36 + 9 = 23$

Step 2.1.2.2

Factor

3

$3$ out of

6 x

$6 x$ .

\frac{7}{3 (3)} (3 (2 x)) + \frac{7}{9} \cdot - 36 + 9 = 23

$\frac{7}{3 (3)} (3 (2 x)) + \frac{7}{9} \cdot - 36 + 9 = 23$

Step 2.1.2.3

Cancel the common factor.

$\frac{7}{3 \cdot 3} (3 (2 x)) + \frac{7}{9} \cdot - 36 + 9 = 23$

Step 2.1.2.4

Rewrite the expression.

$\frac{7}{3} (2 x) + \frac{7}{9} \cdot - 36 + 9 = 23$

Step 2.1.3

Combine

$2$ and

$\frac{7}{3}$ .

$\frac{2 \cdot 7}{3} x + \frac{7}{9} \cdot - 36 + 9 = 23$

Step 2.1.4

Multiply

$2$ by

$7$ .

$\frac{14}{3} x + \frac{7}{9} \cdot - 36 + 9 = 23$

Step 2.1.5

Combine

$\frac{14}{3}$ and

$x$ .

$\frac{14 x}{3} + \frac{7}{9} \cdot - 36 + 9 = 23$

Step 2.1.6

Cancel the common factor of

$9$ .

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Step 2.1.6.1

Factor

$9$ out of

$- 36$ .

$\frac{14 x}{3} + \frac{7}{9} \cdot (9 (- 4)) + 9 = 23$

Step 2.1.6.2

Cancel the common factor.

$\frac{14 x}{3} + \frac{7}{9} \cdot (9 \cdot - 4) + 9 = 23$

Step 2.1.6.3

Rewrite the expression.

$\frac{14 x}{3} + 7 \cdot - 4 + 9 = 23$

Step 2.1.7

Multiply

$7$ by

$- 4$ .

$\frac{14 x}{3} - 28 + 9 = 23$

Step 2.2

Add

$- 28$ and

$9$ .

$\frac{14 x}{3} - 19 = 23$

Step 3

Move all terms not containing

$x$ to the right side of the equation.

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Step 3.1

Add

$19$ to both sides of the equation.

$\frac{14 x}{3} = 23 + 19$

Step 3.2

Add

$23$ and

$19$ .

$\frac{14 x}{3} = 42$

Step 4

Multiply both sides of the equation by

$\frac{3}{14}$ .

$\frac{3}{14} \cdot \frac{14 x}{3} = \frac{3}{14} \cdot 42$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify

$\frac{3}{14} \cdot \frac{14 x}{3}$ .

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Step 5.1.1.1

Cancel the common factor of

$3$ .

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Step 5.1.1.1.1

Cancel the common factor.

$\frac{3}{14} \cdot \frac{14 x}{3} = \frac{3}{14} \cdot 42$

Step 5.1.1.1.2

Rewrite the expression.

$\frac{1}{14} (14 x) = \frac{3}{14} \cdot 42$

Step 5.1.1.2

Cancel the common factor of

$14$ .

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Step 5.1.1.2.1

Factor

$14$ out of

$14 x$ .

$\frac{1}{14} (14 (x)) = \frac{3}{14} \cdot 42$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{1}{14} (14 x) = \frac{3}{14} \cdot 42$

Step 5.1.1.2.3

Rewrite the expression.

$x = \frac{3}{14} \cdot 42$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify

$\frac{3}{14} \cdot 42$ .

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Step 5.2.1.1

Cancel the common factor of

$14$ .

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Step 5.2.1.1.1

Factor

$14$ out of

$42$ .

$x = \frac{3}{14} \cdot (14 (3))$

Step 5.2.1.1.2

Cancel the common factor.

$x = \frac{3}{14} \cdot (14 \cdot 3)$

Step 5.2.1.1.3

Rewrite the expression.

$x = 3 \cdot 3$

Step 5.2.1.2

Multiply

$3$ by

$3$ .

$x = 9$