Algebra Examples

$- 2 (x - 4) - \frac{1}{2} (3 - 4 x) = - 12$

Step 1

Simplify $- 2 (x - 4) - \frac{1}{2} \cdot (3 - 4 x)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$- 2 x - 2 \cdot - 4 - \frac{1}{2} \cdot (3 - 4 x) = - 12$

Step 1.1.2

Multiply $- 2$ by $- 4$ .

$- 2 x + 8 - \frac{1}{2} \cdot (3 - 4 x) = - 12$

Step 1.1.3

Apply the distributive property.

$- 2 x + 8 - \frac{1}{2} \cdot 3 - \frac{1}{2} (- 4 x) = - 12$

Step 1.1.4

Multiply $- \frac{1}{2} \cdot 3$ .

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Step 1.1.4.1

Multiply $3$ by $- 1$ .

$- 2 x + 8 - 3 (\frac{1}{2}) - \frac{1}{2} (- 4 x) = - 12$

Step 1.1.4.2

Combine $- 3$ and $\frac{1}{2}$ .

$- 2 x + 8 + \frac{- 3}{2} - \frac{1}{2} (- 4 x) = - 12$

Step 1.1.5

Cancel the common factor of $2$ .

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Step 1.1.5.1

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

$- 2 x + 8 + \frac{- 3}{2} + \frac{- 1}{2} (- 4 x) = - 12$

Step 1.1.5.2

Factor $2$ out of $- 4 x$ .

$- 2 x + 8 + \frac{- 3}{2} + \frac{- 1}{2} (2 (- 2 x)) = - 12$

Step 1.1.5.3

Cancel the common factor.

$- 2 x + 8 + \frac{- 3}{2} + \frac{- 1}{2} (2 (- 2 x)) = - 12$

Step 1.1.5.4

Rewrite the expression.

$- 2 x + 8 + \frac{- 3}{2} - 1 (- 2 x) = - 12$

Step 1.1.6

Multiply $- 2$ by $- 1$ .

$- 2 x + 8 + \frac{- 3}{2} + 2 x = - 12$

Step 1.1.7

Move the negative in front of the fraction.

$- 2 x + 8 - \frac{3}{2} + 2 x = - 12$

Step 1.2

Combine the opposite terms in $- 2 x + 8 - \frac{3}{2} + 2 x$ .

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Step 1.2.1

Add $- 2 x$ and $2 x$ .

$0 + 8 - \frac{3}{2} = - 12$

Step 1.2.2

Add $0$ and $8$ .

$8 - \frac{3}{2} = - 12$

Step 1.3

To write $8$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$8 \cdot \frac{2}{2} - \frac{3}{2} = - 12$

Step 1.4

Combine $8$ and $\frac{2}{2}$ .

$\frac{8 \cdot 2}{2} - \frac{3}{2} = - 12$

Step 1.5

Combine the numerators over the common denominator.

$\frac{8 \cdot 2 - 3}{2} = - 12$

Step 1.6

Simplify the numerator.

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Step 1.6.1

Multiply $8$ by $2$ .

$\frac{16 - 3}{2} = - 12$

Step 1.6.2

Subtract $3$ from $16$ .

$\frac{13}{2} = - 12$

Step 2

Since $\frac{13}{2} \neq - 12$ , there are no solutions.

No solution