Solve for x (4.5x+x)/2=22

$\frac{4.5 x + x}{2} = 22$

Step 1

Multiply both sides of the equation by $\frac{2}{4.5 + 1}$ .

$\frac{2}{4.5 + 1} \cdot \frac{4.5 x + x}{2} = \frac{2}{4.5 + 1} \cdot 22$

Step 2

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{2}{4.5 + 1} \cdot \frac{4.5 x + x}{2}$ .

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2}{4.5 + 1} \cdot \frac{4.5 x + x}{2} = \frac{2}{4.5 + 1} \cdot 22$

Rewrite the expression.

$\frac{1}{4.5 + 1} (4.5 x + x) = \frac{2}{4.5 + 1} \cdot 22$

Simplify the expression.

Add $4.5$ and $1$ .

$\frac{1}{5.5} (4.5 x + x) = \frac{2}{4.5 + 1} \cdot 22$

Divide $1$ by $5.5$ .

$0.\overline{18} (4.5 x + x) = \frac{2}{4.5 + 1} \cdot 22$

Add $4.5 x$ and $x$ .

$0.\overline{18} (5.5 x) = \frac{2}{4.5 + 1} \cdot 22$

Multiply $5.5$ by $0.\overline{18}$ .

$1 x = \frac{2}{4.5 + 1} \cdot 22$

Simplify the right side.

Simplify $\frac{2}{4.5 + 1} \cdot 22$ .

Add $4.5$ and $1$ .

$1 x = \frac{2}{5.5} \cdot 22$

Cancel the common factor of $5.5$ .

Factor $5.5$ out of $22$ .

$1 x = \frac{2}{5.5} \cdot (5.5 (4))$

Cancel the common factor.

$1 x = \frac{2}{5.5} \cdot (5.5 \cdot 4)$

Rewrite the expression.

$1 x = 2 \cdot 4$

Multiply $2$ by $4$ .

$1 x = 8$

Step 3

Divide each term in $1 x = 8$ by $1$ and simplify.

Divide each term in $1 x = 8$ by $1$ .

$\frac{1 x}{1} = \frac{8}{1}$

Simplify the left side.

Cancel the common factor of $1$ .

Cancel the common factor.

$\frac{1 x}{1} = \frac{8}{1}$

Divide $x$ by $1$ .

$x = \frac{8}{1}$

Simplify the right side.

Divide $8$ by $1$ .

$x = 8$

Solve for x (4.5x+x)/2=22

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