Solve for x 5(x+2)=7(4-x)

$5 (x + 2) = 7 (4 - x)$

Step 1

Simplify $5 (x + 2)$ .

Rewrite.

$0 + 0 + 5 (x + 2) = 7 (4 - x)$

Simplify by adding zeros.

$5 (x + 2) = 7 (4 - x)$

Apply the distributive property.

$5 x + 5 \cdot 2 = 7 (4 - x)$

Multiply $5$ by $2$ .

$5 x + 10 = 7 (4 - x)$

Step 2

Simplify $7 (4 - x)$ .

Apply the distributive property.

$5 x + 10 = 7 \cdot 4 + 7 (- x)$

Multiply.

Multiply $7$ by $4$ .

$5 x + 10 = 28 + 7 (- x)$

Multiply $- 1$ by $7$ .

$5 x + 10 = 28 - 7 x$

Step 3

Move all terms containing $x$ to the left side of the equation.

Add $7 x$ to both sides of the equation.

$5 x + 10 + 7 x = 28$

Add $5 x$ and $7 x$ .

$12 x + 10 = 28$

Step 4

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

Subtract $10$ from both sides of the equation.

$12 x = 28 - 10$

Subtract $10$ from $28$ .

$12 x = 18$

Step 5

Divide each term in $12 x = 18$ by $12$ and simplify.

Divide each term in $12 x = 18$ by $12$ .

$\frac{12 x}{12} = \frac{18}{12}$

Simplify the left side.

Cancel the common factor of $12$ .

Cancel the common factor.

$\frac{12 x}{12} = \frac{18}{12}$

Divide $x$ by $1$ .

$x = \frac{18}{12}$

Simplify the right side.

Cancel the common factor of $18$ and $12$ .

Factor $6$ out of $18$ .

$x = \frac{6 (3)}{12}$

Cancel the common factors.

Factor $6$ out of $12$ .

$x = \frac{6 \cdot 3}{6 \cdot 2}$

Cancel the common factor.

$x = \frac{6 \cdot 3}{6 \cdot 2}$

Rewrite the expression.

$x = \frac{3}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3}{2}$

Decimal Form:

$x = 1.5$

Mixed Number Form:

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

Solve for x 5(x+2)=7(4-x)

Related Questions

Support LCMGCF.com by disabling your adblocker.