Solve for x 3(x+2)+4(x-5)=10

$3 (x + 2) + 4 (x - 5) = 10$

Step 1

Simplify $3 (x + 2) + 4 (x - 5)$ .

Simplify each term.

Apply the distributive property.

$3 x + 3 \cdot 2 + 4 (x - 5) = 10$

Multiply $3$ by $2$ .

$3 x + 6 + 4 (x - 5) = 10$

Apply the distributive property.

$3 x + 6 + 4 x + 4 \cdot - 5 = 10$

Multiply $4$ by $- 5$ .

$3 x + 6 + 4 x - 20 = 10$

Simplify by adding terms.

Add $3 x$ and $4 x$ .

$7 x + 6 - 20 = 10$

Subtract $20$ from $6$ .

$7 x - 14 = 10$

Step 2

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

Add $14$ to both sides of the equation.

$7 x = 10 + 14$

Add $10$ and $14$ .

$7 x = 24$

Step 3

Divide each term in $7 x = 24$ by $7$ and simplify.

Divide each term in $7 x = 24$ by $7$ .

$\frac{7 x}{7} = \frac{24}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{24}{7}$

Divide $x$ by $1$ .

$x = \frac{24}{7}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{24}{7}$

Decimal Form:

$x = 3.\overline{428571}$

Mixed Number Form:

$x = 3 \frac{3}{7}$