Solve for x 3/8x-6=1/2(4-x)

$\frac{3}{8} x - 6 = \frac{1}{2} (4 - x)$

Step 1

Combine $\frac{3}{8}$ and $x$ .

$\frac{3 x}{8} - 6 = \frac{1}{2} \cdot (4 - x)$

Step 2

Simplify $\frac{1}{2} \cdot (4 - x)$ .

Apply the distributive property.

$\frac{3 x}{8} - 6 = \frac{1}{2} \cdot 4 + \frac{1}{2} (- x)$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$\frac{3 x}{8} - 6 = \frac{1}{2} \cdot (2 (2)) + \frac{1}{2} (- x)$

Cancel the common factor.

$\frac{3 x}{8} - 6 = \frac{1}{2} \cdot (2 \cdot 2) + \frac{1}{2} (- x)$

Rewrite the expression.

$\frac{3 x}{8} - 6 = 2 + \frac{1}{2} (- x)$

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

$\frac{3 x}{8} - 6 = 2 - \frac{x}{2}$

Step 3

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

Add $\frac{x}{2}$ to both sides of the equation.

$\frac{3 x}{8} - 6 + \frac{x}{2} = 2$

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

$\frac{3 x}{8} + \frac{x}{2} \cdot \frac{4}{4} - 6 = 2$

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{x}{2}$ by $\frac{4}{4}$ .

$\frac{3 x}{8} + \frac{x \cdot 4}{2 \cdot 4} - 6 = 2$

Multiply $2$ by $4$ .

$\frac{3 x}{8} + \frac{x \cdot 4}{8} - 6 = 2$

Combine the numerators over the common denominator.

$\frac{3 x + x \cdot 4}{8} - 6 = 2$

Add $3 x$ and $x \cdot 4$ .

Reorder $x$ and $4$ .

$\frac{3 x + 4 \cdot x}{8} - 6 = 2$

Add $3 x$ and $4 \cdot x$ .

$\frac{7 x}{8} - 6 = 2$

Step 4

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

Add $6$ to both sides of the equation.

$\frac{7 x}{8} = 2 + 6$

Add $2$ and $6$ .

$\frac{7 x}{8} = 8$

Step 5

Multiply both sides of the equation by $\frac{8}{7}$ .

$\frac{8}{7} \cdot \frac{7 x}{8} = \frac{8}{7} \cdot 8$

Step 6

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{8}{7} \cdot \frac{7 x}{8}$ .

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8}{7} \cdot \frac{7 x}{8} = \frac{8}{7} \cdot 8$

Rewrite the expression.

$\frac{1}{7} (7 x) = \frac{8}{7} \cdot 8$

Cancel the common factor of $7$ .

Factor $7$ out of $7 x$ .

$\frac{1}{7} (7 (x)) = \frac{8}{7} \cdot 8$

Cancel the common factor.

$\frac{1}{7} (7 x) = \frac{8}{7} \cdot 8$

Rewrite the expression.

$x = \frac{8}{7} \cdot 8$

Simplify the right side.

Multiply $\frac{8}{7} \cdot 8$ .

Combine $\frac{8}{7}$ and $8$ .

$x = \frac{8 \cdot 8}{7}$

Multiply $8$ by $8$ .

$x = \frac{64}{7}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \frac{64}{7}$

Decimal Form:

$x = 9.\overline{142857}$

Mixed Number Form:

$x = 9 \frac{1}{7}$

Solve for x 3/8x-6=1/2(4-x)

Related Questions

Support LCMGCF.com by disabling your adblocker.