Solve for x 1/4x-2=-6+5/12x

$\frac{1}{4} x - 2 = - 6 + \frac{5}{12} x$

Step 1

Combine $\frac{1}{4}$ and $x$ .

$\frac{x}{4} - 2 = - 6 + \frac{5}{12} x$

Step 2

Combine $\frac{5}{12}$ and $x$ .

$\frac{x}{4} - 2 = - 6 + \frac{5 x}{12}$

Step 3

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

Subtract $\frac{5 x}{12}$ from both sides of the equation.

$\frac{x}{4} - 2 - \frac{5 x}{12} = - 6$

To write $\frac{x}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{x}{4} \cdot \frac{3}{3} - \frac{5 x}{12} - 2 = - 6$

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{x}{4}$ by $\frac{3}{3}$ .

$\frac{x \cdot 3}{4 \cdot 3} - \frac{5 x}{12} - 2 = - 6$

Multiply $4$ by $3$ .

$\frac{x \cdot 3}{12} - \frac{5 x}{12} - 2 = - 6$

Combine the numerators over the common denominator.

$\frac{x \cdot 3 - 5 x}{12} - 2 = - 6$

Subtract $5 x$ from $x \cdot 3$ .

Reorder $x$ and $3$ .

$\frac{3 \cdot x - 5 x}{12} - 2 = - 6$

Subtract $5 x$ from $3 \cdot x$ .

$\frac{- 2 \cdot x}{12} - 2 = - 6$

Simplify each term.

Cancel the common factor of $- 2$ and $12$ .

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

$\frac{2 (- x)}{12} - 2 = - 6$

Cancel the common factors.

Factor $2$ out of $12$ .

$\frac{2 (- x)}{2 (6)} - 2 = - 6$

Cancel the common factor.

$\frac{2 (- x)}{2 \cdot 6} - 2 = - 6$

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Step 4

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

Add $2$ to both sides of the equation.

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

Add $- 6$ and $2$ .

$- \frac{x}{6} = - 4$

Step 5

Multiply both sides of the equation by $- 6$ .

$- 6 (- \frac{x}{6}) = - 6 \cdot - 4$

Step 6

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 6 (- \frac{x}{6})$ .

Cancel the common factor of $6$ .

Move the leading negative in $- \frac{x}{6}$ into the numerator.

$- 6 \frac{- x}{6} = - 6 \cdot - 4$

Factor $6$ out of $- 6$ .

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

Cancel the common factor.

$6 \cdot - 1 \frac{- x}{6} = - 6 \cdot - 4$

Rewrite the expression.

$- - x = - 6 \cdot - 4$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - 6 \cdot - 4$

Multiply $x$ by $1$ .

$x = - 6 \cdot - 4$

Simplify the right side.

Multiply $- 6$ by $- 4$ .

$x = 24$

Solve for x 1/4x-2=-6+5/12x

Related Questions

Support LCMGCF.com by disabling your adblocker.