Algebra Examples

$- 10 + 7 (4 x - \frac{1}{2}) = - \frac{1}{2} - 2 x$

Step 1

Simplify $- 10 + 7 (4 x - \frac{1}{2})$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$- 10 + 7 (4 x) + 7 (- \frac{1}{2}) = - \frac{1}{2} - 2 x$

Step 1.1.2

Multiply $4$ by $7$ .

$- 10 + 28 x + 7 (- \frac{1}{2}) = - \frac{1}{2} - 2 x$

Step 1.1.3

Multiply $7 (- \frac{1}{2})$ .

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Step 1.1.3.1

Multiply $- 1$ by $7$ .

$- 10 + 28 x - 7 (\frac{1}{2}) = - \frac{1}{2} - 2 x$

Step 1.1.3.2

Combine $- 7$ and $\frac{1}{2}$ .

$- 10 + 28 x + \frac{- 7}{2} = - \frac{1}{2} - 2 x$

Step 1.1.4

Move the negative in front of the fraction.

$- 10 + 28 x - \frac{7}{2} = - \frac{1}{2} - 2 x$

Step 1.2

To write $- 10$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$28 x - 10 \cdot \frac{2}{2} - \frac{7}{2} = - \frac{1}{2} - 2 x$

Step 1.3

Combine $- 10$ and $\frac{2}{2}$ .

$28 x + \frac{- 10 \cdot 2}{2} - \frac{7}{2} = - \frac{1}{2} - 2 x$

Step 1.4

Combine the numerators over the common denominator.

$28 x + \frac{- 10 \cdot 2 - 7}{2} = - \frac{1}{2} - 2 x$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $- 10$ by $2$ .

$28 x + \frac{- 20 - 7}{2} = - \frac{1}{2} - 2 x$

Step 1.5.2

Subtract $7$ from $- 20$ .

$28 x + \frac{- 27}{2} = - \frac{1}{2} - 2 x$

Step 1.6

Move the negative in front of the fraction.

$28 x - \frac{27}{2} = - \frac{1}{2} - 2 x$

Step 2

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

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Step 2.1

Add $2 x$ to both sides of the equation.

$28 x - \frac{27}{2} + 2 x = - \frac{1}{2}$

Step 2.2

Add $28 x$ and $2 x$ .

$30 x - \frac{27}{2} = - \frac{1}{2}$

Step 3

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

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Step 3.1

Add $\frac{27}{2}$ to both sides of the equation.

$30 x = - \frac{1}{2} + \frac{27}{2}$

Step 3.2

Combine the numerators over the common denominator.

$30 x = \frac{- 1 + 27}{2}$

Step 3.3

Add $- 1$ and $27$ .

$30 x = \frac{26}{2}$

Step 3.4

Divide $26$ by $2$ .

$30 x = 13$

Step 4

Divide each term in $30 x = 13$ by $30$ and simplify.

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Step 4.1

Divide each term in $30 x = 13$ by $30$ .

$\frac{30 x}{30} = \frac{13}{30}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $30$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{30 x}{30} = \frac{13}{30}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{13}{30}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{13}{30}$

Decimal Form:

$x = 0.4\overline{3}$