Solve for x (2x-7)/4+2x-(4x-9)/3=x/2

$\frac{2 x - 7}{4} + 2 x - \frac{4 x - 9}{3} = \frac{x}{2}$

Step 1

Multiply both sides by $2$ .

$(\frac{2 x - 7}{4} + 2 x - \frac{4 x - 9}{3}) \cdot 2 = \frac{x}{2} \cdot 2$

Step 2

Simplify.

Simplify the left side.

Simplify $(\frac{2 x - 7}{4} + 2 x - \frac{4 x - 9}{3}) \cdot 2$ .

Find the common denominator.

Multiply $\frac{2 x - 7}{4}$ by $\frac{3}{3}$ .

$(\frac{2 x - 7}{4} \cdot \frac{3}{3} + 2 x - \frac{4 x - 9}{3}) \cdot 2 = \frac{x}{2} \cdot 2$

Multiply $\frac{2 x - 7}{4}$ by $\frac{3}{3}$ .

$(\frac{(2 x - 7) \cdot 3}{4 \cdot 3} + 2 x - \frac{4 x - 9}{3}) \cdot 2 = \frac{x}{2} \cdot 2$

Write $2 x$ as a fraction with denominator $1$ .

$(\frac{(2 x - 7) \cdot 3}{4 \cdot 3} + \frac{2 x}{1} - \frac{4 x - 9}{3}) \cdot 2 = \frac{x}{2} \cdot 2$

Multiply $\frac{2 x}{1}$ by $\frac{12}{12}$ .

$(\frac{(2 x - 7) \cdot 3}{4 \cdot 3} + \frac{2 x}{1} \cdot \frac{12}{12} - \frac{4 x - 9}{3}) \cdot 2 = \frac{x}{2} \cdot 2$

Multiply $\frac{2 x}{1}$ by $\frac{12}{12}$ .

$(\frac{(2 x - 7) \cdot 3}{4 \cdot 3} + \frac{2 x \cdot 12}{12} - \frac{4 x - 9}{3}) \cdot 2 = \frac{x}{2} \cdot 2$

Multiply $\frac{4 x - 9}{3}$ by $\frac{4}{4}$ .

$(\frac{(2 x - 7) \cdot 3}{4 \cdot 3} + \frac{2 x \cdot 12}{12} - (\frac{4 x - 9}{3} \cdot \frac{4}{4})) \cdot 2 = \frac{x}{2} \cdot 2$

Multiply $\frac{4 x - 9}{3}$ by $\frac{4}{4}$ .

$(\frac{(2 x - 7) \cdot 3}{4 \cdot 3} + \frac{2 x \cdot 12}{12} - \frac{(4 x - 9) \cdot 4}{3 \cdot 4}) \cdot 2 = \frac{x}{2} \cdot 2$

Reorder the factors of $4 \cdot 3$ .

$(\frac{(2 x - 7) \cdot 3}{3 \cdot 4} + \frac{2 x \cdot 12}{12} - \frac{(4 x - 9) \cdot 4}{3 \cdot 4}) \cdot 2 = \frac{x}{2} \cdot 2$

Multiply $3$ by $4$ .

$(\frac{(2 x - 7) \cdot 3}{12} + \frac{2 x \cdot 12}{12} - \frac{(4 x - 9) \cdot 4}{3 \cdot 4}) \cdot 2 = \frac{x}{2} \cdot 2$

Multiply $3$ by $4$ .

$(\frac{(2 x - 7) \cdot 3}{12} + \frac{2 x \cdot 12}{12} - \frac{(4 x - 9) \cdot 4}{12}) \cdot 2 = \frac{x}{2} \cdot 2$

Combine the numerators over the common denominator.

$\frac{(2 x - 7) \cdot 3 + 2 x \cdot 12 - (4 x - 9) \cdot 4}{12} \cdot 2 = \frac{x}{2} \cdot 2$

Simplify each term.

Apply the distributive property.

$\frac{2 x \cdot 3 - 7 \cdot 3 + 2 x \cdot 12 - (4 x - 9) \cdot 4}{12} \cdot 2 = \frac{x}{2} \cdot 2$

Multiply $3$ by $2$ .

$\frac{6 x - 7 \cdot 3 + 2 x \cdot 12 - (4 x - 9) \cdot 4}{12} \cdot 2 = \frac{x}{2} \cdot 2$

Multiply $- 7$ by $3$ .

$\frac{6 x - 21 + 2 x \cdot 12 - (4 x - 9) \cdot 4}{12} \cdot 2 = \frac{x}{2} \cdot 2$

Multiply $12$ by $2$ .

$\frac{6 x - 21 + 24 x - (4 x - 9) \cdot 4}{12} \cdot 2 = \frac{x}{2} \cdot 2$

Apply the distributive property.

$\frac{6 x - 21 + 24 x + (- (4 x) - - 9) \cdot 4}{12} \cdot 2 = \frac{x}{2} \cdot 2$

Multiply $4$ by $- 1$ .

$\frac{6 x - 21 + 24 x + (- 4 x - - 9) \cdot 4}{12} \cdot 2 = \frac{x}{2} \cdot 2$

Multiply $- 1$ by $- 9$ .

$\frac{6 x - 21 + 24 x + (- 4 x + 9) \cdot 4}{12} \cdot 2 = \frac{x}{2} \cdot 2$

Apply the distributive property.

$\frac{6 x - 21 + 24 x - 4 x \cdot 4 + 9 \cdot 4}{12} \cdot 2 = \frac{x}{2} \cdot 2$

Multiply $4$ by $- 4$ .

$\frac{6 x - 21 + 24 x - 16 x + 9 \cdot 4}{12} \cdot 2 = \frac{x}{2} \cdot 2$

Multiply $9$ by $4$ .

$\frac{6 x - 21 + 24 x - 16 x + 36}{12} \cdot 2 = \frac{x}{2} \cdot 2$

Simplify terms.

Add $6 x$ and $24 x$ .

$\frac{30 x - 21 - 16 x + 36}{12} \cdot 2 = \frac{x}{2} \cdot 2$

Subtract $16 x$ from $30 x$ .

$\frac{14 x - 21 + 36}{12} \cdot 2 = \frac{x}{2} \cdot 2$

Add $- 21$ and $36$ .

$\frac{14 x + 15}{12} \cdot 2 = \frac{x}{2} \cdot 2$

Cancel the common factor of $2$ .

Factor $2$ out of $12$ .

$\frac{14 x + 15}{2 (6)} \cdot 2 = \frac{x}{2} \cdot 2$

Cancel the common factor.

$\frac{14 x + 15}{2 \cdot 6} \cdot 2 = \frac{x}{2} \cdot 2$

Rewrite the expression.

$\frac{14 x + 15}{6} = \frac{x}{2} \cdot 2$

Simplify the right side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{14 x + 15}{6} = \frac{x}{2} \cdot 2$

Rewrite the expression.

$\frac{14 x + 15}{6} = x$

Step 3

Solve for $x$ .

Multiply both sides by $6$ .

$\frac{14 x + 15}{6} \cdot 6 = x \cdot 6$

Simplify.

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{14 x + 15}{6} \cdot 6 = x \cdot 6$

Rewrite the expression.

$14 x + 15 = x \cdot 6$

Simplify the right side.

Move $6$ to the left of $x$ .

$14 x + 15 = 6 x$

Solve for $x$ .

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

Subtract $6 x$ from both sides of the equation.

$14 x + 15 - 6 x = 0$

Subtract $6 x$ from $14 x$ .

$8 x + 15 = 0$

Subtract $15$ from both sides of the equation.

$8 x = - 15$

Divide each term in $8 x = - 15$ by $8$ and simplify.

Divide each term in $8 x = - 15$ by $8$ .

$\frac{8 x}{8} = \frac{- 15}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x}{8} = \frac{- 15}{8}$

Divide $x$ by $1$ .

$x = \frac{- 15}{8}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{15}{8}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{15}{8}$

Decimal Form:

$x = - 1.875$

Mixed Number Form:

$x = - 1 \frac{7}{8}$

Solve for x (2x-7)/4+2x-(4x-9)/3=x/2

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