Algebra Examples

$\frac{3 x}{2} + \frac{5}{8} = \frac{x}{4}$

Step 1

Multiply both sides by $4$ .

$(\frac{3 x}{2} + \frac{5}{8}) \cdot 4 = \frac{x}{4} \cdot 4$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(\frac{3 x}{2} + \frac{5}{8}) \cdot 4$ .

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Step 2.1.1.1

Apply the distributive property.

$\frac{3 x}{2} \cdot 4 + \frac{5}{8} \cdot 4 = \frac{x}{4} \cdot 4$

Step 2.1.1.2

Cancel the common factor of $2$ .

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Step 2.1.1.2.1

Factor $2$ out of $4$ .

$\frac{3 x}{2} \cdot (2 (2)) + \frac{5}{8} \cdot 4 = \frac{x}{4} \cdot 4$

Step 2.1.1.2.2

Cancel the common factor.

$\frac{3 x}{2} \cdot (2 \cdot 2) + \frac{5}{8} \cdot 4 = \frac{x}{4} \cdot 4$

Step 2.1.1.2.3

Rewrite the expression.

$3 x \cdot 2 + \frac{5}{8} \cdot 4 = \frac{x}{4} \cdot 4$

Step 2.1.1.3

Multiply $2$ by $3$ .

$6 x + \frac{5}{8} \cdot 4 = \frac{x}{4} \cdot 4$

Step 2.1.1.4

Cancel the common factor of $4$ .

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Step 2.1.1.4.1

Factor $4$ out of $8$ .

$6 x + \frac{5}{4 (2)} \cdot 4 = \frac{x}{4} \cdot 4$

Step 2.1.1.4.2

Cancel the common factor.

$6 x + \frac{5}{4 \cdot 2} \cdot 4 = \frac{x}{4} \cdot 4$

Step 2.1.1.4.3

Rewrite the expression.

$6 x + \frac{5}{2} = \frac{x}{4} \cdot 4$

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $4$ .

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Step 2.2.1.1

Cancel the common factor.

$6 x + \frac{5}{2} = \frac{x}{4} \cdot 4$

Step 2.2.1.2

Rewrite the expression.

$6 x + \frac{5}{2} = x$

Step 3

Solve for $x$ .

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Step 3.1

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

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Step 3.1.1

Subtract $x$ from both sides of the equation.

$6 x + \frac{5}{2} - x = 0$

Step 3.1.2

Subtract $x$ from $6 x$ .

$5 x + \frac{5}{2} = 0$

Step 3.2

Subtract $\frac{5}{2}$ from both sides of the equation.

$5 x = - \frac{5}{2}$

Step 3.3

Divide each term in $5 x = - \frac{5}{2}$ by $5$ and simplify.

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Step 3.3.1

Divide each term in $5 x = - \frac{5}{2}$ by $5$ .

$\frac{5 x}{5} = \frac{- \frac{5}{2}}{5}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $5$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{- \frac{5}{2}}{5}$

Step 3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- \frac{5}{2}}{5}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{5}{2} \cdot \frac{1}{5}$

Step 3.3.3.2

Cancel the common factor of $5$ .

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Step 3.3.3.2.1

Move the leading negative in $- \frac{5}{2}$ into the numerator.

$x = \frac{- 5}{2} \cdot \frac{1}{5}$

Step 3.3.3.2.2

Factor $5$ out of $- 5$ .

$x = \frac{5 (- 1)}{2} \cdot \frac{1}{5}$

Step 3.3.3.2.3

Cancel the common factor.

$x = \frac{5 \cdot - 1}{2} \cdot \frac{1}{5}$

Step 3.3.3.2.4

Rewrite the expression.

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

Step 3.3.3.3

Move the negative in front of the fraction.

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = - 0.5$