Solve for x 5/8x+1/16x=11/16+x

$\frac{5}{8} x + \frac{1}{16} x = \frac{11}{16} + x$

Step 1

Simplify $\frac{5}{8} x + \frac{1}{16} x$ .

Simplify each term.

Combine $\frac{5}{8}$ and $x$ .

$\frac{5 x}{8} + \frac{1}{16} x = \frac{11}{16} + x$

Combine $\frac{1}{16}$ and $x$ .

$\frac{5 x}{8} + \frac{x}{16} = \frac{11}{16} + x$

To write $\frac{5 x}{8}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

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

Multiply $\frac{5 x}{8}$ by $\frac{2}{2}$ .

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

Multiply $8$ by $2$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Factor $x$ out of $5 x \cdot 2 + x$ .

Factor $x$ out of $5 x \cdot 2$ .

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

Raise $x$ to the power of $1$ .

$\frac{x (5 \cdot 2) + x^{1}}{16} = \frac{11}{16} + x$

Factor $x$ out of $x^{1}$ .

$\frac{x (5 \cdot 2) + x \cdot 1}{16} = \frac{11}{16} + x$

Factor $x$ out of $x (5 \cdot 2) + x \cdot 1$ .

$\frac{x (5 \cdot 2 + 1)}{16} = \frac{11}{16} + x$

Multiply $5$ by $2$ .

$\frac{x (10 + 1)}{16} = \frac{11}{16} + x$

Add $10$ and $1$ .

$\frac{x \cdot 11}{16} = \frac{11}{16} + x$

Move $11$ to the left of $x$ .

$\frac{11 x}{16} = \frac{11}{16} + x$

Step 2

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

Subtract $x$ from both sides of the equation.

$\frac{11 x}{16} - x = \frac{11}{16}$

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

$\frac{11 x}{16} - x \cdot \frac{16}{16} = \frac{11}{16}$

Combine $- x$ and $\frac{16}{16}$ .

$\frac{11 x}{16} + \frac{- x \cdot 16}{16} = \frac{11}{16}$

Combine the numerators over the common denominator.

$\frac{11 x - x \cdot 16}{16} = \frac{11}{16}$

Simplify the numerator.

Factor $x$ out of $11 x - x \cdot 16$ .

Factor $x$ out of $11 x$ .

$\frac{x \cdot 11 - x \cdot 16}{16} = \frac{11}{16}$

Factor $x$ out of $- x \cdot 16$ .

$\frac{x \cdot 11 + x (- 1 \cdot 16)}{16} = \frac{11}{16}$

Factor $x$ out of $x \cdot 11 + x (- 1 \cdot 16)$ .

$\frac{x (11 - 1 \cdot 16)}{16} = \frac{11}{16}$

Multiply $- 1$ by $16$ .

$\frac{x (11 - 16)}{16} = \frac{11}{16}$

Subtract $16$ from $11$ .

$\frac{x \cdot - 5}{16} = \frac{11}{16}$

Move $- 5$ to the left of $x$ .

$\frac{- 5 \cdot x}{16} = \frac{11}{16}$

Move the negative in front of the fraction.

$- \frac{5 x}{16} = \frac{11}{16}$

Step 3

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

$- 5 x = 11$

Step 4

Divide each term in $- 5 x = 11$ by $- 5$ and simplify.

Divide each term in $- 5 x = 11$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{11}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{11}{- 5}$

Divide $x$ by $1$ .

$x = \frac{11}{- 5}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{11}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{11}{5}$

Decimal Form:

$x = - 2.2$

Mixed Number Form:

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

Solve for x 5/8x+1/16x=11/16+x

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