Solve for x 7/2x-2=28-4x

$\frac{7}{2} x - 2 = 28 - 4 x$

Step 1

Combine $\frac{7}{2}$ and $x$ .

$\frac{7 x}{2} - 2 = 28 - 4 x$

Step 2

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

Add $4 x$ to both sides of the equation.

$\frac{7 x}{2} - 2 + 4 x = 28$

To write $4 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{7 x}{2} + 4 x \cdot \frac{2}{2} - 2 = 28$

Combine $4 x$ and $\frac{2}{2}$ .

$\frac{7 x}{2} + \frac{4 x \cdot 2}{2} - 2 = 28$

Combine the numerators over the common denominator.

$\frac{7 x + 4 x \cdot 2}{2} - 2 = 28$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $7 x + 4 x \cdot 2$ .

Factor $x$ out of $7 x$ .

$\frac{x \cdot 7 + 4 x \cdot 2}{2} - 2 = 28$

Factor $x$ out of $4 x \cdot 2$ .

$\frac{x \cdot 7 + x (4 \cdot 2)}{2} - 2 = 28$

Factor $x$ out of $x \cdot 7 + x (4 \cdot 2)$ .

$\frac{x (7 + 4 \cdot 2)}{2} - 2 = 28$

Multiply $4$ by $2$ .

$\frac{x (7 + 8)}{2} - 2 = 28$

Add $7$ and $8$ .

$\frac{x \cdot 15}{2} - 2 = 28$

Move $15$ to the left of $x$ .

$\frac{15 x}{2} - 2 = 28$

Step 3

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

Add $2$ to both sides of the equation.

$\frac{15 x}{2} = 28 + 2$

Add $28$ and $2$ .

$\frac{15 x}{2} = 30$

Step 4

Multiply both sides of the equation by $\frac{2}{15}$ .

$\frac{2}{15} \cdot \frac{15 x}{2} = \frac{2}{15} \cdot 30$

Step 5

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{2}{15} \cdot \frac{15 x}{2}$ .

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2}{15} \cdot \frac{15 x}{2} = \frac{2}{15} \cdot 30$

Rewrite the expression.

$\frac{1}{15} (15 x) = \frac{2}{15} \cdot 30$

Cancel the common factor of $15$ .

Factor $15$ out of $15 x$ .

$\frac{1}{15} (15 (x)) = \frac{2}{15} \cdot 30$

Cancel the common factor.

$\frac{1}{15} (15 x) = \frac{2}{15} \cdot 30$

Rewrite the expression.

$x = \frac{2}{15} \cdot 30$

Simplify the right side.

Simplify $\frac{2}{15} \cdot 30$ .

Cancel the common factor of $15$ .

Factor $15$ out of $30$ .

$x = \frac{2}{15} \cdot (15 (2))$

Cancel the common factor.

$x = \frac{2}{15} \cdot (15 \cdot 2)$

Rewrite the expression.

$x = 2 \cdot 2$

Multiply $2$ by $2$ .

$x = 4$

Solve for x 7/2x-2=28-4x

Related Questions

Support LCMGCF.com by disabling your adblocker.