Algebra Examples

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

Step 1

Simplify the left side.

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Step 1.1

Convert $2 \frac{7}{8}$ to an improper fraction.

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Step 1.1.1

A mixed number is an addition of its whole and fractional parts.

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

Step 1.1.2

Add $2$ and $\frac{7}{8}$ .

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Step 1.1.2.1

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

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

Step 1.1.2.2

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

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

Step 1.1.2.3

Combine the numerators over the common denominator.

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

Step 1.1.2.4

Simplify the numerator.

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Step 1.1.2.4.1

Multiply $2$ by $8$ .

$\frac{16 + 7}{8} = \frac{3}{4} \cdot (z + 1)$

Step 1.1.2.4.2

Add $16$ and $7$ .

$\frac{23}{8} = \frac{3}{4} \cdot (z + 1)$

Step 2

Simplify the right side.

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Step 2.1

Simplify $\frac{3}{4} \cdot (z + 1)$ .

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Step 2.1.1

Apply the distributive property.

$\frac{23}{8} = \frac{3}{4} z + \frac{3}{4} \cdot 1$

Step 2.1.2

Combine $\frac{3}{4}$ and $z$ .

$\frac{23}{8} = \frac{3 z}{4} + \frac{3}{4} \cdot 1$

Step 2.1.3

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

$\frac{23}{8} = \frac{3 z}{4} + \frac{3}{4}$

Step 3

Rewrite the equation as $\frac{3 z}{4} + \frac{3}{4} = \frac{23}{8}$ .

$\frac{3 z}{4} + \frac{3}{4} = \frac{23}{8}$

Step 4

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

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Step 4.1

Subtract $\frac{3}{4}$ from both sides of the equation.

$\frac{3 z}{4} = \frac{23}{8} - \frac{3}{4}$

Step 4.2

To write $- \frac{3}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3 z}{4} = \frac{23}{8} - \frac{3}{4} \cdot \frac{2}{2}$

Step 4.3

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

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Step 4.3.1

Multiply $\frac{3}{4}$ by $\frac{2}{2}$ .

$\frac{3 z}{4} = \frac{23}{8} - \frac{3 \cdot 2}{4 \cdot 2}$

Step 4.3.2

Multiply $4$ by $2$ .

$\frac{3 z}{4} = \frac{23}{8} - \frac{3 \cdot 2}{8}$

Step 4.4

Combine the numerators over the common denominator.

$\frac{3 z}{4} = \frac{23 - 3 \cdot 2}{8}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $- 3$ by $2$ .

$\frac{3 z}{4} = \frac{23 - 6}{8}$

Step 4.5.2

Subtract $6$ from $23$ .

$\frac{3 z}{4} = \frac{17}{8}$

Step 5

Multiply both sides of the equation by $\frac{4}{3}$ .

$\frac{4}{3} \cdot \frac{3 z}{4} = \frac{4}{3} \cdot \frac{17}{8}$

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Simplify $\frac{4}{3} \cdot \frac{3 z}{4}$ .

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Step 6.1.1.1

Cancel the common factor of $4$ .

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Step 6.1.1.1.1

Cancel the common factor.

$\frac{4}{3} \cdot \frac{3 z}{4} = \frac{4}{3} \cdot \frac{17}{8}$

Step 6.1.1.1.2

Rewrite the expression.

$\frac{1}{3} (3 z) = \frac{4}{3} \cdot \frac{17}{8}$

Step 6.1.1.2

Cancel the common factor of $3$ .

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Step 6.1.1.2.1

Factor $3$ out of $3 z$ .

$\frac{1}{3} (3 (z)) = \frac{4}{3} \cdot \frac{17}{8}$

Step 6.1.1.2.2

Cancel the common factor.

$\frac{1}{3} (3 z) = \frac{4}{3} \cdot \frac{17}{8}$

Step 6.1.1.2.3

Rewrite the expression.

$z = \frac{4}{3} \cdot \frac{17}{8}$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $\frac{4}{3} \cdot \frac{17}{8}$ .

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Step 6.2.1.1

Cancel the common factor of $4$ .

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Step 6.2.1.1.1

Factor $4$ out of $8$ .

$z = \frac{4}{3} \cdot \frac{17}{4 (2)}$

Step 6.2.1.1.2

Cancel the common factor.

$z = \frac{4}{3} \cdot \frac{17}{4 \cdot 2}$

Step 6.2.1.1.3

Rewrite the expression.

$z = \frac{1}{3} \cdot \frac{17}{2}$

Step 6.2.1.2

Multiply $\frac{1}{3}$ by $\frac{17}{2}$ .

$z = \frac{17}{3 \cdot 2}$

Step 6.2.1.3

Multiply $3$ by $2$ .

$z = \frac{17}{6}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$z = \frac{17}{6}$

Decimal Form:

$z = 2.8\overline{3}$

Mixed Number Form:

$z = 2 \frac{5}{6}$