Algebra Examples

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

Step 1

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

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Step 1.1

Rewrite.

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

Step 1.2

Rewrite.

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

Step 1.3

Simplify by adding terms.

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

Step 1.4

Simplify each term.

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Step 1.4.1

Apply the distributive property.

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

Step 1.4.2

Cancel the common factor of $2$ .

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Step 1.4.2.1

Factor $2$ out of $4 x$ .

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

Step 1.4.2.2

Cancel the common factor.

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

Step 1.4.2.3

Rewrite the expression.

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

Step 1.4.3

Multiply $2$ by $3$ .

$6 x + \frac{3}{2} \cdot - 1 + 8 x = - (4 x + \frac{1}{2}) + 4 x$

Step 1.4.4

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

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Step 1.4.4.1

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

$6 x + \frac{3 \cdot - 1}{2} + 8 x = - (4 x + \frac{1}{2}) + 4 x$

Step 1.4.4.2

Multiply $3$ by $- 1$ .

$6 x + \frac{- 3}{2} + 8 x = - (4 x + \frac{1}{2}) + 4 x$

Step 1.4.5

Move the negative in front of the fraction.

$6 x - \frac{3}{2} + 8 x = - (4 x + \frac{1}{2}) + 4 x$

Step 1.5

Add $6 x$ and $8 x$ .

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

Step 2

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

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

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

Step 2.1.2

Multiply $4$ by $- 1$ .

$14 x - \frac{3}{2} = - 4 x - \frac{1}{2} + 4 x$

Step 2.2

Combine the opposite terms in $- 4 x - \frac{1}{2} + 4 x$ .

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Step 2.2.1

Add $- 4 x$ and $4 x$ .

$14 x - \frac{3}{2} = 0 - \frac{1}{2}$

Step 2.2.2

Subtract $\frac{1}{2}$ from $0$ .

$14 x - \frac{3}{2} = - \frac{1}{2}$

Step 3

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

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Step 3.1

Add $\frac{3}{2}$ to both sides of the equation.

$14 x = - \frac{1}{2} + \frac{3}{2}$

Step 3.2

Combine the numerators over the common denominator.

$14 x = \frac{- 1 + 3}{2}$

Step 3.3

Add $- 1$ and $3$ .

$14 x = \frac{2}{2}$

Step 3.4

Divide $2$ by $2$ .

$14 x = 1$

Step 4

Divide each term in $14 x = 1$ by $14$ and simplify.

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Step 4.1

Divide each term in $14 x = 1$ by $14$ .

$\frac{14 x}{14} = \frac{1}{14}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $14$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{14 x}{14} = \frac{1}{14}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{1}{14}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{14}$

Decimal Form:

$x = 0.0\overline{714285}$