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

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

Step 1

Combine $\frac{7}{4}$ and $x$ .

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

Step 2

Combine $\frac{9}{2}$ and $x$ .

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

Step 3

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

Subtract $\frac{9 x}{2}$ from both sides of the equation.

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

To write $- \frac{9 x}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{9 x}{2}$ by $\frac{2}{2}$ .

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

Multiply $2$ by $2$ .

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

Combine the numerators over the common denominator.

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

Simplify each term.

Simplify the numerator.

Factor $x$ out of $7 x - 9 x \cdot 2$ .

Factor $x$ out of $7 x$ .

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

Factor $x$ out of $- 9 x \cdot 2$ .

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

Factor $x$ out of $x \cdot 7 + x (- 9 \cdot 2)$ .

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

Multiply $- 9$ by $2$ .

$\frac{x (7 - 18)}{4} - 3 = 2$

Subtract $18$ from $7$ .

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

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

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

Move the negative in front of the fraction.

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

Step 4

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

Add $3$ to both sides of the equation.

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

Add $2$ and $3$ .

$- \frac{11 x}{4} = 5$

Step 5

Multiply both sides of the equation by $- \frac{4}{11}$ .

$- \frac{4}{11} (- \frac{11 x}{4}) = - \frac{4}{11} \cdot 5$

Step 6

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{4}{11} (- \frac{11 x}{4})$ .

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{4}{11}$ into the numerator.

$\frac{- 4}{11} (- \frac{11 x}{4}) = - \frac{4}{11} \cdot 5$

Move the leading negative in $- \frac{11 x}{4}$ into the numerator.

$\frac{- 4}{11} \cdot \frac{- 11 x}{4} = - \frac{4}{11} \cdot 5$

Factor $4$ out of $- 4$ .

$\frac{4 (- 1)}{11} \cdot \frac{- 11 x}{4} = - \frac{4}{11} \cdot 5$

Cancel the common factor.

$\frac{4 \cdot - 1}{11} \cdot \frac{- 11 x}{4} = - \frac{4}{11} \cdot 5$

Rewrite the expression.

$\frac{- 1}{11} (- 11 x) = - \frac{4}{11} \cdot 5$

Cancel the common factor of $11$ .

Factor $11$ out of $- 11 x$ .

$\frac{- 1}{11} (11 (- x)) = - \frac{4}{11} \cdot 5$

Cancel the common factor.

$\frac{- 1}{11} (11 (- x)) = - \frac{4}{11} \cdot 5$

Rewrite the expression.

$- - x = - \frac{4}{11} \cdot 5$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{4}{11} \cdot 5$

Multiply $x$ by $1$ .

$x = - \frac{4}{11} \cdot 5$

Simplify the right side.

Simplify $- \frac{4}{11} \cdot 5$ .

Multiply $- \frac{4}{11} \cdot 5$ .

Multiply $5$ by $- 1$ .

$x = - 5 (\frac{4}{11})$

Combine $- 5$ and $\frac{4}{11}$ .

$x = \frac{- 5 \cdot 4}{11}$

Multiply $- 5$ by $4$ .

$x = \frac{- 20}{11}$

Move the negative in front of the fraction.

$x = - \frac{20}{11}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{20}{11}$

Decimal Form:

$x = - 1.\overline{81}$

Mixed Number Form:

$x = - 1 \frac{9}{11}$

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

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