Pre-Algebra Examples

$\frac{2}{3} \cdot (6 x - 9) = - 34$

Step 1

Multiply both sides of the equation by $\frac{3}{2}$ .

$\frac{3}{2} (\frac{2}{3} \cdot (6 x - 9)) = \frac{3}{2} \cdot - 34$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{3}{2} (\frac{2}{3} \cdot (6 x - 9))$ .

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Step 2.1.1.1

Apply the distributive property.

$\frac{3}{2} (\frac{2}{3} (6 x) + \frac{2}{3} \cdot - 9) = \frac{3}{2} \cdot - 34$

Step 2.1.1.2

Cancel the common factor of $3$ .

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Step 2.1.1.2.1

Factor $3$ out of $6 x$ .

$\frac{3}{2} (\frac{2}{3} (3 (2 x)) + \frac{2}{3} \cdot - 9) = \frac{3}{2} \cdot - 34$

Step 2.1.1.2.2

Cancel the common factor.

$\frac{3}{2} (\frac{2}{3} (3 (2 x)) + \frac{2}{3} \cdot - 9) = \frac{3}{2} \cdot - 34$

Step 2.1.1.2.3

Rewrite the expression.

$\frac{3}{2} (2 (2 x) + \frac{2}{3} \cdot - 9) = \frac{3}{2} \cdot - 34$

Step 2.1.1.3

Multiply $2$ by $2$ .

$\frac{3}{2} (4 x + \frac{2}{3} \cdot - 9) = \frac{3}{2} \cdot - 34$

Step 2.1.1.4

Cancel the common factor of $3$ .

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Step 2.1.1.4.1

Factor $3$ out of $- 9$ .

$\frac{3}{2} (4 x + \frac{2}{3} \cdot (3 (- 3))) = \frac{3}{2} \cdot - 34$

Step 2.1.1.4.2

Cancel the common factor.

$\frac{3}{2} (4 x + \frac{2}{3} \cdot (3 \cdot - 3)) = \frac{3}{2} \cdot - 34$

Step 2.1.1.4.3

Rewrite the expression.

$\frac{3}{2} (4 x + 2 \cdot - 3) = \frac{3}{2} \cdot - 34$

Step 2.1.1.5

Multiply $2$ by $- 3$ .

$\frac{3}{2} (4 x - 6) = \frac{3}{2} \cdot - 34$

Step 2.1.1.6

Apply the distributive property.

$\frac{3}{2} (4 x) + \frac{3}{2} \cdot - 6 = \frac{3}{2} \cdot - 34$

Step 2.1.1.7

Cancel the common factor of $2$ .

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Step 2.1.1.7.1

Factor $2$ out of $4 x$ .

$\frac{3}{2} (2 (2 x)) + \frac{3}{2} \cdot - 6 = \frac{3}{2} \cdot - 34$

Step 2.1.1.7.2

Cancel the common factor.

$\frac{3}{2} (2 (2 x)) + \frac{3}{2} \cdot - 6 = \frac{3}{2} \cdot - 34$

Step 2.1.1.7.3

Rewrite the expression.

$3 (2 x) + \frac{3}{2} \cdot - 6 = \frac{3}{2} \cdot - 34$

Step 2.1.1.8

Multiply $2$ by $3$ .

$6 x + \frac{3}{2} \cdot - 6 = \frac{3}{2} \cdot - 34$

Step 2.1.1.9

Cancel the common factor of $2$ .

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Step 2.1.1.9.1

Factor $2$ out of $- 6$ .

$6 x + \frac{3}{2} \cdot (2 (- 3)) = \frac{3}{2} \cdot - 34$

Step 2.1.1.9.2

Cancel the common factor.

$6 x + \frac{3}{2} \cdot (2 \cdot - 3) = \frac{3}{2} \cdot - 34$

Step 2.1.1.9.3

Rewrite the expression.

$6 x + 3 \cdot - 3 = \frac{3}{2} \cdot - 34$

Step 2.1.1.10

Multiply $3$ by $- 3$ .

$6 x - 9 = \frac{3}{2} \cdot - 34$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{3}{2} \cdot - 34$ .

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Step 2.2.1.1

Cancel the common factor of $2$ .

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Step 2.2.1.1.1

Factor $2$ out of $- 34$ .

$6 x - 9 = \frac{3}{2} \cdot (2 (- 17))$

Step 2.2.1.1.2

Cancel the common factor.

$6 x - 9 = \frac{3}{2} \cdot (2 \cdot - 17)$

Step 2.2.1.1.3

Rewrite the expression.

$6 x - 9 = 3 \cdot - 17$

Step 2.2.1.2

Multiply $3$ by $- 17$ .

$6 x - 9 = - 51$

Step 3

Move all terms not containing $x$ to the right side of the equation.

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Step 3.1

Add $9$ to both sides of the equation.

$6 x = - 51 + 9$

Step 3.2

Add $- 51$ and $9$ .

$6 x = - 42$

Step 4

Divide each term in $6 x = - 42$ by $6$ and simplify.

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Step 4.1

Divide each term in $6 x = - 42$ by $6$ .

$\frac{6 x}{6} = \frac{- 42}{6}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $6$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{6 x}{6} = \frac{- 42}{6}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 42}{6}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 42$ by $6$ .

$x = - 7$