Solve for x 1/2(x+8)+3/2x=10

$\frac{1}{2} (x + 8) + \frac{3}{2} x = 10$

Step 1

Simplify $\frac{1}{2} \cdot (x + 8) + \frac{3}{2} x$ .

Simplify each term.

Apply the distributive property.

$\frac{1}{2} x + \frac{1}{2} \cdot 8 + \frac{3}{2} x = 10$

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

$\frac{x}{2} + \frac{1}{2} \cdot 8 + \frac{3}{2} x = 10$

Cancel the common factor of $2$ .

Factor $2$ out of $8$ .

$\frac{x}{2} + \frac{1}{2} \cdot (2 (4)) + \frac{3}{2} x = 10$

Cancel the common factor.

$\frac{x}{2} + \frac{1}{2} \cdot (2 \cdot 4) + \frac{3}{2} x = 10$

Rewrite the expression.

$\frac{x}{2} + 4 + \frac{3}{2} x = 10$

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

$\frac{x}{2} + 4 + \frac{3 x}{2} = 10$

Simplify terms.

Combine the numerators over the common denominator.

$4 + \frac{x + 3 x}{2} = 10$

Add $x$ and $3 x$ .

$4 + \frac{4 x}{2} = 10$

Cancel the common factor of $4$ and $2$ .

Factor $2$ out of $4 x$ .

$4 + \frac{2 (2 x)}{2} = 10$

Cancel the common factors.

Factor $2$ out of $2$ .

$4 + \frac{2 (2 x)}{2 (1)} = 10$

Cancel the common factor.

$4 + \frac{2 (2 x)}{2 \cdot 1} = 10$

Rewrite the expression.

$4 + \frac{2 x}{1} = 10$

Divide $2 x$ by $1$ .

$4 + 2 x = 10$

Step 2

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

Subtract $4$ from both sides of the equation.

$2 x = 10 - 4$

Subtract $4$ from $10$ .

$2 x = 6$

Step 3

Divide each term in $2 x = 6$ by $2$ and simplify.

Divide each term in $2 x = 6$ by $2$ .

$\frac{2 x}{2} = \frac{6}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{6}{2}$

Divide $x$ by $1$ .

$x = \frac{6}{2}$

Simplify the right side.

Divide $6$ by $2$ .

$x = 3$

Solve for x 1/2(x+8)+3/2x=10

Related Questions

Support LCMGCF.com by disabling your adblocker.