Solve for z 3 15/16=7/8(z+3)

$3 \frac{15}{16} = \frac{7}{8} (z + 3)$

Simplify the left side.

Convert $3 \frac{15}{16}$ to an improper fraction.

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

$3 + \frac{15}{16} = \frac{7}{8} \cdot (z + 3)$

Add $3$ and $\frac{15}{16}$ .

To write $3$ as a fraction with a common denominator, multiply by $\frac{16}{16}$ .

$3 \cdot \frac{16}{16} + \frac{15}{16} = \frac{7}{8} \cdot (z + 3)$

Combine $3$ and $\frac{16}{16}$ .

$\frac{3 \cdot 16}{16} + \frac{15}{16} = \frac{7}{8} \cdot (z + 3)$

Combine the numerators over the common denominator.

$\frac{3 \cdot 16 + 15}{16} = \frac{7}{8} \cdot (z + 3)$

Simplify the numerator.

Multiply $3$ by $16$ .

$\frac{48 + 15}{16} = \frac{7}{8} \cdot (z + 3)$

Add $48$ and $15$ .

$\frac{63}{16} = \frac{7}{8} \cdot (z + 3)$

Simplify the right side.

Simplify $\frac{7}{8} \cdot (z + 3)$ .

Apply the distributive property.

$\frac{63}{16} = \frac{7}{8} z + \frac{7}{8} \cdot 3$

Combine $\frac{7}{8}$ and $z$ .

$\frac{63}{16} = \frac{7 z}{8} + \frac{7}{8} \cdot 3$

Multiply $\frac{7}{8} \cdot 3$ .

Combine $\frac{7}{8}$ and $3$ .

$\frac{63}{16} = \frac{7 z}{8} + \frac{7 \cdot 3}{8}$

Multiply $7$ by $3$ .

$\frac{63}{16} = \frac{7 z}{8} + \frac{21}{8}$

Rewrite the equation as $\frac{7 z}{8} + \frac{21}{8} = \frac{63}{16}$ .

$\frac{7 z}{8} + \frac{21}{8} = \frac{63}{16}$

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

Subtract $\frac{21}{8}$ from both sides of the equation.

$\frac{7 z}{8} = \frac{63}{16} - \frac{21}{8}$

To write $- \frac{21}{8}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{7 z}{8} = \frac{63}{16} - \frac{21}{8} \cdot \frac{2}{2}$

Write each expression with a common denominator of $16$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{21}{8}$ by $\frac{2}{2}$ .

$\frac{7 z}{8} = \frac{63}{16} - \frac{21 \cdot 2}{8 \cdot 2}$

Multiply $8$ by $2$ .

$\frac{7 z}{8} = \frac{63}{16} - \frac{21 \cdot 2}{16}$

Combine the numerators over the common denominator.

$\frac{7 z}{8} = \frac{63 - 21 \cdot 2}{16}$

Simplify the numerator.

Multiply $- 21$ by $2$ .

$\frac{7 z}{8} = \frac{63 - 42}{16}$

Subtract $42$ from $63$ .

$\frac{7 z}{8} = \frac{21}{16}$

Multiply both sides of the equation by $\frac{8}{7}$ .

$\frac{8}{7} \cdot \frac{7 z}{8} = \frac{8}{7} \cdot \frac{21}{16}$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{8}{7} \cdot \frac{7 z}{8}$ .

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8}{7} \cdot \frac{7 z}{8} = \frac{8}{7} \cdot \frac{21}{16}$

Rewrite the expression.

$\frac{1}{7} (7 z) = \frac{8}{7} \cdot \frac{21}{16}$

Cancel the common factor of $7$ .

Factor $7$ out of $7 z$ .

$\frac{1}{7} (7 (z)) = \frac{8}{7} \cdot \frac{21}{16}$

Cancel the common factor.

$\frac{1}{7} (7 z) = \frac{8}{7} \cdot \frac{21}{16}$

Rewrite the expression.

$z = \frac{8}{7} \cdot \frac{21}{16}$

Simplify the right side.

Simplify $\frac{8}{7} \cdot \frac{21}{16}$ .

Cancel the common factor of $8$ .

Factor $8$ out of $16$ .

$z = \frac{8}{7} \cdot \frac{21}{8 (2)}$

Cancel the common factor.

$z = \frac{8}{7} \cdot \frac{21}{8 \cdot 2}$

Rewrite the expression.

$z = \frac{1}{7} \cdot \frac{21}{2}$

Cancel the common factor of $7$ .

Factor $7$ out of $21$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$z = 1.5$

Mixed Number Form:

$z = 1 \frac{1}{2}$

Solve for z 3 15/16=7/8(z+3)

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