Solve for z (11z)/16+(7z)/8=5/16

$\frac{11 z}{16} + \frac{7 z}{8} = \frac{5}{16}$

Step 1

Simplify $\frac{11 z}{16} + \frac{7 z}{8}$ .

To write $\frac{7 z}{8}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{11 z}{16} + \frac{7 z}{8} \cdot \frac{2}{2} = \frac{5}{16}$

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

Multiply $\frac{7 z}{8}$ by $\frac{2}{2}$ .

$\frac{11 z}{16} + \frac{7 z \cdot 2}{8 \cdot 2} = \frac{5}{16}$

Multiply $8$ by $2$ .

$\frac{11 z}{16} + \frac{7 z \cdot 2}{16} = \frac{5}{16}$

Combine the numerators over the common denominator.

$\frac{11 z + 7 z \cdot 2}{16} = \frac{5}{16}$

Simplify the numerator.

Factor $z$ out of $11 z + 7 z \cdot 2$ .

Factor $z$ out of $11 z$ .

$\frac{z \cdot 11 + 7 z \cdot 2}{16} = \frac{5}{16}$

Factor $z$ out of $7 z \cdot 2$ .

$\frac{z \cdot 11 + z (7 \cdot 2)}{16} = \frac{5}{16}$

Factor $z$ out of $z \cdot 11 + z (7 \cdot 2)$ .

$\frac{z (11 + 7 \cdot 2)}{16} = \frac{5}{16}$

Multiply $7$ by $2$ .

$\frac{z (11 + 14)}{16} = \frac{5}{16}$

Add $11$ and $14$ .

$\frac{z \cdot 25}{16} = \frac{5}{16}$

Move $25$ to the left of $z$ .

$\frac{25 z}{16} = \frac{5}{16}$

Step 2

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$25 z = 5$

Step 3

Divide each term in $25 z = 5$ by $25$ and simplify.

Divide each term in $25 z = 5$ by $25$ .

$\frac{25 z}{25} = \frac{5}{25}$

Simplify the left side.

Cancel the common factor of $25$ .

Cancel the common factor.

$\frac{25 z}{25} = \frac{5}{25}$

Divide $z$ by $1$ .

$z = \frac{5}{25}$

Simplify the right side.

Cancel the common factor of $5$ and $25$ .

Factor $5$ out of $5$ .

$z = \frac{5 (1)}{25}$

Cancel the common factors.

Factor $5$ out of $25$ .

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

Cancel the common factor.

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

Rewrite the expression.

$z = \frac{1}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$z = \frac{1}{5}$

Decimal Form:

$z = 0.2$

Solve for z (11z)/16+(7z)/8=5/16

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