Pre-Algebra Examples

$\frac{2}{3} \cdot (21 x + 27) - 7 = - \frac{1}{2} \cdot (4 x - 18)$

Step 1

Simplify $\frac{2}{3} \cdot (21 x + 27) - 7$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$\frac{2}{3} (21 x) + \frac{2}{3} \cdot 27 - 7 = - \frac{1}{2} \cdot (4 x - 18)$

Step 1.1.2

Cancel the common factor of $3$ .

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Step 1.1.2.1

Factor $3$ out of $21 x$ .

$\frac{2}{3} (3 (7 x)) + \frac{2}{3} \cdot 27 - 7 = - \frac{1}{2} \cdot (4 x - 18)$

Step 1.1.2.2

Cancel the common factor.

$\frac{2}{3} (3 (7 x)) + \frac{2}{3} \cdot 27 - 7 = - \frac{1}{2} \cdot (4 x - 18)$

Step 1.1.2.3

Rewrite the expression.

$2 (7 x) + \frac{2}{3} \cdot 27 - 7 = - \frac{1}{2} \cdot (4 x - 18)$

Step 1.1.3

Multiply $7$ by $2$ .

$14 x + \frac{2}{3} \cdot 27 - 7 = - \frac{1}{2} \cdot (4 x - 18)$

Step 1.1.4

Cancel the common factor of $3$ .

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Step 1.1.4.1

Factor $3$ out of $27$ .

$14 x + \frac{2}{3} \cdot (3 (9)) - 7 = - \frac{1}{2} \cdot (4 x - 18)$

Step 1.1.4.2

Cancel the common factor.

$14 x + \frac{2}{3} \cdot (3 \cdot 9) - 7 = - \frac{1}{2} \cdot (4 x - 18)$

Step 1.1.4.3

Rewrite the expression.

$14 x + 2 \cdot 9 - 7 = - \frac{1}{2} \cdot (4 x - 18)$

Step 1.1.5

Multiply $2$ by $9$ .

$14 x + 18 - 7 = - \frac{1}{2} \cdot (4 x - 18)$

Step 1.2

Subtract $7$ from $18$ .

$14 x + 11 = - \frac{1}{2} \cdot (4 x - 18)$

Step 2

Simplify $- \frac{1}{2} \cdot (4 x - 18)$ .

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Step 2.1

Apply the distributive property.

$14 x + 11 = - \frac{1}{2} (4 x) - \frac{1}{2} \cdot - 18$

Step 2.2

Cancel the common factor of $2$ .

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Step 2.2.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$14 x + 11 = \frac{- 1}{2} (4 x) - \frac{1}{2} \cdot - 18$

Step 2.2.2

Factor $2$ out of $4 x$ .

$14 x + 11 = \frac{- 1}{2} (2 (2 x)) - \frac{1}{2} \cdot - 18$

Step 2.2.3

Cancel the common factor.

$14 x + 11 = \frac{- 1}{2} (2 (2 x)) - \frac{1}{2} \cdot - 18$

Step 2.2.4

Rewrite the expression.

$14 x + 11 = - 1 (2 x) - \frac{1}{2} \cdot - 18$

Step 2.3

Multiply $2$ by $- 1$ .

$14 x + 11 = - 2 x - \frac{1}{2} \cdot - 18$

Step 2.4

Cancel the common factor of $2$ .

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Step 2.4.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$14 x + 11 = - 2 x + \frac{- 1}{2} \cdot - 18$

Step 2.4.2

Factor $2$ out of $- 18$ .

$14 x + 11 = - 2 x + \frac{- 1}{2} \cdot (2 (- 9))$

Step 2.4.3

Cancel the common factor.

$14 x + 11 = - 2 x + \frac{- 1}{2} \cdot (2 \cdot - 9)$

Step 2.4.4

Rewrite the expression.

$14 x + 11 = - 2 x - 1 \cdot - 9$

Step 2.5

Multiply $- 1$ by $- 9$ .

$14 x + 11 = - 2 x + 9$

Step 3

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x = - \frac{1}{8}$

Step 4