Solve for x -3/4x-11/4x=-7/2

$- \frac{3}{4} x - \frac{11}{4} x = - \frac{7}{2}$

Step 1

Simplify $- \frac{3}{4} x - \frac{11}{4} x$ .

Simplify each term.

Combine $x$ and $\frac{3}{4}$ .

$- \frac{x \cdot 3}{4} - \frac{11}{4} x = - \frac{7}{2}$

Move $3$ to the left of $x$ .

$- \frac{3 \cdot x}{4} - \frac{11}{4} x = - \frac{7}{2}$

Combine $x$ and $\frac{11}{4}$ .

$- \frac{3 x}{4} - \frac{x \cdot 11}{4} = - \frac{7}{2}$

Move $11$ to the left of $x$ .

$- \frac{3 x}{4} - \frac{11 x}{4} = - \frac{7}{2}$

Simplify terms.

Combine the numerators over the common denominator.

$\frac{- 3 x - 11 x}{4} = - \frac{7}{2}$

Subtract $11 x$ from $- 3 x$ .

$\frac{- 14 x}{4} = - \frac{7}{2}$

Cancel the common factor of $- 14$ and $4$ .

Factor $2$ out of $- 14 x$ .

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

Cancel the common factors.

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Step 2

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$- 7 x = - 7$

Step 3

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

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

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

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 7$ by $- 7$ .

$x = 1$