Solve for x 8(x+1/2)=44

$8 (x + \frac{1}{2}) = 44$

Step 1

Simplify.

Apply the distributive property.

$8 x + 8 (\frac{1}{2}) = 44$

Cancel the common factor of $2$ .

Factor $2$ out of $8$ .

$8 x + 2 (4) \frac{1}{2} = 44$

Cancel the common factor.

$8 x + 2 \cdot 4 \frac{1}{2} = 44$

Rewrite the expression.

$8 x + 4 = 44$

Step 2

Divide each term in $(8 x + 4) = 44$ by $8$ and simplify.

Divide each term in $(8 x + 4) = 44$ by $8$ .

$\frac{(8 x + 4)}{8} = \frac{44}{8}$

Simplify the left side.

Cancel the common factor of $8 x + 4$ and $8$ .

Factor $4$ out of $8 x$ .

$\frac{4 (2 x) + 4}{8} = \frac{44}{8}$

Factor $4$ out of $4$ .

$\frac{4 (2 x) + 4 (1)}{8} = \frac{44}{8}$

Factor $4$ out of $4 (2 x) + 4 (1)$ .

$\frac{4 (2 x + 1)}{8} = \frac{44}{8}$

Cancel the common factors.

Factor $4$ out of $8$ .

$\frac{4 (2 x + 1)}{4 (2)} = \frac{44}{8}$

Cancel the common factor.

$\frac{4 (2 x + 1)}{4 \cdot 2} = \frac{44}{8}$

Rewrite the expression.

$\frac{2 x + 1}{2} = \frac{44}{8}$

Simplify the right side.

Cancel the common factor of $44$ and $8$ .

Factor $4$ out of $44$ .

$\frac{2 x + 1}{2} = \frac{4 (11)}{8}$

Cancel the common factors.

Factor $4$ out of $8$ .

$\frac{2 x + 1}{2} = \frac{4 \cdot 11}{4 \cdot 2}$

Cancel the common factor.

$\frac{2 x + 1}{2} = \frac{4 \cdot 11}{4 \cdot 2}$

Rewrite the expression.

$\frac{2 x + 1}{2} = \frac{11}{2}$

Step 3

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

$2 x + 1 = 11$

Step 4

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

Subtract $1$ from both sides of the equation.

$2 x = 11 - 1$

Subtract $1$ from $11$ .

$2 x = 10$

Step 5

Divide each term in $2 x = 10$ by $2$ and simplify.

Divide each term in $2 x = 10$ by $2$ .

$\frac{2 x}{2} = \frac{10}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{10}{2}$

Divide $x$ by $1$ .

$x = \frac{10}{2}$

Simplify the right side.

Divide $10$ by $2$ .

$x = 5$

Solve for x 8(x+1/2)=44

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