Algebra Examples

$\frac{3 z}{2} + \frac{1}{4} = \frac{7}{8}$

Step 1

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

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Step 1.1

Subtract $\frac{1}{4}$ from both sides of the equation.

$\frac{3 z}{2} = \frac{7}{8} - \frac{1}{4}$

Step 1.2

To write $- \frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3 z}{2} = \frac{7}{8} - \frac{1}{4} \cdot \frac{2}{2}$

Step 1.3

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{1}{4}$ by $\frac{2}{2}$ .

$\frac{3 z}{2} = \frac{7}{8} - \frac{2}{4 \cdot 2}$

Step 1.3.2

Multiply $4$ by $2$ .

$\frac{3 z}{2} = \frac{7}{8} - \frac{2}{8}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{3 z}{2} = \frac{7 - 2}{8}$

Step 1.5

Subtract $2$ from $7$ .

$\frac{3 z}{2} = \frac{5}{8}$

Step 2

Multiply both sides of the equation by $\frac{2}{3}$ .

$\frac{2}{3} \cdot \frac{3 z}{2} = \frac{2}{3} \cdot \frac{5}{8}$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{2}{3} \cdot \frac{3 z}{2}$ .

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Step 3.1.1.1

Cancel the common factor of $2$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{2}{3} \cdot \frac{3 z}{2} = \frac{2}{3} \cdot \frac{5}{8}$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{3} (3 z) = \frac{2}{3} \cdot \frac{5}{8}$

Step 3.1.1.2

Cancel the common factor of $3$ .

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Step 3.1.1.2.1

Factor $3$ out of $3 z$ .

$\frac{1}{3} (3 (z)) = \frac{2}{3} \cdot \frac{5}{8}$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{1}{3} (3 z) = \frac{2}{3} \cdot \frac{5}{8}$

Step 3.1.1.2.3

Rewrite the expression.

$z = \frac{2}{3} \cdot \frac{5}{8}$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{2}{3} \cdot \frac{5}{8}$ .

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Step 3.2.1.1

Cancel the common factor of $2$ .

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Step 3.2.1.1.1

Factor $2$ out of $8$ .

$z = \frac{2}{3} \cdot \frac{5}{2 (4)}$

Step 3.2.1.1.2

Cancel the common factor.

$z = \frac{2}{3} \cdot \frac{5}{2 \cdot 4}$

Step 3.2.1.1.3

Rewrite the expression.

$z = \frac{1}{3} \cdot \frac{5}{4}$

Step 3.2.1.2

Multiply $\frac{1}{3}$ by $\frac{5}{4}$ .

$z = \frac{5}{3 \cdot 4}$

Step 3.2.1.3

Multiply $3$ by $4$ .

$z = \frac{5}{12}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$z = \frac{5}{12}$

Decimal Form:

$z = 0.41\overline{6}$