Algebra Examples

$14 x - \frac{1}{2} (4 x + 6) = 3 (x - 4) - 18$

Step 1

Simplify $14 x - \frac{1}{2} \cdot (4 x + 6)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$14 x - \frac{1}{2} (4 x) - \frac{1}{2} \cdot 6 = 3 (x - 4) - 18$

Step 1.1.2

Cancel the common factor of $2$ .

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Step 1.1.2.1

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

$14 x + \frac{- 1}{2} (4 x) - \frac{1}{2} \cdot 6 = 3 (x - 4) - 18$

Step 1.1.2.2

Factor $2$ out of $4 x$ .

$14 x + \frac{- 1}{2} (2 (2 x)) - \frac{1}{2} \cdot 6 = 3 (x - 4) - 18$

Step 1.1.2.3

Cancel the common factor.

$14 x + \frac{- 1}{2} (2 (2 x)) - \frac{1}{2} \cdot 6 = 3 (x - 4) - 18$

Step 1.1.2.4

Rewrite the expression.

$14 x - 1 (2 x) - \frac{1}{2} \cdot 6 = 3 (x - 4) - 18$

Step 1.1.3

Multiply $2$ by $- 1$ .

$14 x - 2 x - \frac{1}{2} \cdot 6 = 3 (x - 4) - 18$

Step 1.1.4

Cancel the common factor of $2$ .

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Step 1.1.4.1

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

$14 x - 2 x + \frac{- 1}{2} \cdot 6 = 3 (x - 4) - 18$

Step 1.1.4.2

Factor $2$ out of $6$ .

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

Step 1.1.4.3

Cancel the common factor.

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

Step 1.1.4.4

Rewrite the expression.

$14 x - 2 x - 1 \cdot 3 = 3 (x - 4) - 18$

Step 1.1.5

Multiply $- 1$ by $3$ .

$14 x - 2 x - 3 = 3 (x - 4) - 18$

Step 1.2

Subtract $2 x$ from $14 x$ .

$12 x - 3 = 3 (x - 4) - 18$

Step 2

Simplify $3 (x - 4) - 18$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$12 x - 3 = 3 x + 3 \cdot - 4 - 18$

Step 2.1.2

Multiply $3$ by $- 4$ .

$12 x - 3 = 3 x - 12 - 18$

Step 2.2

Subtract $18$ from $- 12$ .

$12 x - 3 = 3 x - 30$

Step 3

Move all terms containing $x$ to the left side of the equation.

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Step 3.1

Subtract $3 x$ from both sides of the equation.

$12 x - 3 - 3 x = - 30$

Step 3.2

Subtract $3 x$ from $12 x$ .

$9 x - 3 = - 30$

Step 4

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

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Step 4.1

Add $3$ to both sides of the equation.

$9 x = - 30 + 3$

Step 4.2

Add $- 30$ and $3$ .

$9 x = - 27$

Step 5

Divide each term in $9 x = - 27$ by $9$ and simplify.

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Step 5.1

Divide each term in $9 x = - 27$ by $9$ .

$\frac{9 x}{9} = \frac{- 27}{9}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $9$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{9 x}{9} = \frac{- 27}{9}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 27}{9}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $- 27$ by $9$ .

$x = - 3$