Solve for x (3x+17)+(1/2x-5)=180

$(3 x + 17) + (\frac{1}{2} x - 5) = 180$

Step 1

Simplify $3 x + 17 + \frac{1}{2} x - 5$ .

Combine $\frac{1}{2}$ and $x$ .

$3 x + 17 + \frac{x}{2} - 5 = 180$

To write $3 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$3 x \cdot \frac{2}{2} + \frac{x}{2} + 17 - 5 = 180$

Combine $3 x$ and $\frac{2}{2}$ .

$\frac{3 x \cdot 2}{2} + \frac{x}{2} + 17 - 5 = 180$

Combine the numerators over the common denominator.

$\frac{3 x \cdot 2 + x}{2} + 17 - 5 = 180$

Find the common denominator.

Write $17$ as a fraction with denominator $1$ .

$\frac{3 x \cdot 2 + x}{2} + \frac{17}{1} - 5 = 180$

Multiply $\frac{17}{1}$ by $\frac{2}{2}$ .

$\frac{3 x \cdot 2 + x}{2} + \frac{17}{1} \cdot \frac{2}{2} - 5 = 180$

Multiply $\frac{17}{1}$ by $\frac{2}{2}$ .

$\frac{3 x \cdot 2 + x}{2} + \frac{17 \cdot 2}{2} - 5 = 180$

Write $- 5$ as a fraction with denominator $1$ .

$\frac{3 x \cdot 2 + x}{2} + \frac{17 \cdot 2}{2} + \frac{- 5}{1} = 180$

Multiply $\frac{- 5}{1}$ by $\frac{2}{2}$ .

$\frac{3 x \cdot 2 + x}{2} + \frac{17 \cdot 2}{2} + \frac{- 5}{1} \cdot \frac{2}{2} = 180$

Multiply $\frac{- 5}{1}$ by $\frac{2}{2}$ .

$\frac{3 x \cdot 2 + x}{2} + \frac{17 \cdot 2}{2} + \frac{- 5 \cdot 2}{2} = 180$

Combine the numerators over the common denominator.

$\frac{3 x \cdot 2 + x + 17 \cdot 2 - 5 \cdot 2}{2} = 180$

Simplify each term.

Multiply $2$ by $3$ .

$\frac{6 x + x + 17 \cdot 2 - 5 \cdot 2}{2} = 180$

Multiply $17$ by $2$ .

$\frac{6 x + x + 34 - 5 \cdot 2}{2} = 180$

Multiply $- 5$ by $2$ .

$\frac{6 x + x + 34 - 10}{2} = 180$

Simplify by adding terms.

Add $6 x$ and $x$ .

$\frac{7 x + 34 - 10}{2} = 180$

Subtract $10$ from $34$ .

$\frac{7 x + 24}{2} = 180$

Step 2

Multiply both sides by $2$ .

$\frac{7 x + 24}{2} \cdot 2 = 180 \cdot 2$

Step 3

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{7 x + 24}{2} \cdot 2 = 180 \cdot 2$

Rewrite the expression.

$7 x + 24 = 180 \cdot 2$

Simplify the right side.

Multiply $180$ by $2$ .

$7 x + 24 = 360$

Step 4

Solve for $x$ .

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

Subtract $24$ from both sides of the equation.

$7 x = 360 - 24$

Subtract $24$ from $360$ .

$7 x = 336$

Divide each term in $7 x = 336$ by $7$ and simplify.

Divide each term in $7 x = 336$ by $7$ .

$\frac{7 x}{7} = \frac{336}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{336}{7}$

Divide $x$ by $1$ .

$x = \frac{336}{7}$

Simplify the right side.

Divide $336$ by $7$ .

$x = 48$

Solve for x (3x+17)+(1/2x-5)=180

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