Solve for x 7 1/4x-x=9 3/8

$7 \frac{1}{4} x - x = 9 \frac{3}{8}$

Simplify the left side.

Simplify $7 \frac{1}{4} x - x$ .

Convert $7 \frac{1}{4}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$(7 + \frac{1}{4}) x - x = 9 \frac{3}{8}$

Add $7$ and $\frac{1}{4}$ .

To write $7$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$(7 \cdot \frac{4}{4} + \frac{1}{4}) x - x = 9 \frac{3}{8}$

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

$(\frac{7 \cdot 4}{4} + \frac{1}{4}) x - x = 9 \frac{3}{8}$

Combine the numerators over the common denominator.

$\frac{7 \cdot 4 + 1}{4} x - x = 9 \frac{3}{8}$

Simplify the numerator.

Multiply $7$ by $4$ .

$\frac{28 + 1}{4} x - x = 9 \frac{3}{8}$

Add $28$ and $1$ .

$\frac{29}{4} x - x = 9 \frac{3}{8}$

Combine $\frac{29}{4}$ and $x$ .

$\frac{29 x}{4} - x = 9 \frac{3}{8}$

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

$\frac{29 x}{4} - x \cdot \frac{4}{4} = 9 \frac{3}{8}$

Simplify terms.

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

$\frac{29 x}{4} + \frac{- x \cdot 4}{4} = 9 \frac{3}{8}$

Combine the numerators over the common denominator.

$\frac{29 x - x \cdot 4}{4} = 9 \frac{3}{8}$

Simplify the numerator.

Factor $x$ out of $29 x - x \cdot 4$ .

Factor $x$ out of $29 x$ .

$\frac{x \cdot 29 - x \cdot 4}{4} = 9 \frac{3}{8}$

Factor $x$ out of $- x \cdot 4$ .

$\frac{x \cdot 29 + x (- 1 \cdot 4)}{4} = 9 \frac{3}{8}$

Factor $x$ out of $x \cdot 29 + x (- 1 \cdot 4)$ .

$\frac{x (29 - 1 \cdot 4)}{4} = 9 \frac{3}{8}$

Multiply $- 1$ by $4$ .

$\frac{x (29 - 4)}{4} = 9 \frac{3}{8}$

Subtract $4$ from $29$ .

$\frac{x \cdot 25}{4} = 9 \frac{3}{8}$

Move $25$ to the left of $x$ .

$\frac{25 x}{4} = 9 \frac{3}{8}$

Simplify the right side.

Convert $9 \frac{3}{8}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$\frac{25 x}{4} = 9 + \frac{3}{8}$

Add $9$ and $\frac{3}{8}$ .

To write $9$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{25 x}{4} = 9 \cdot \frac{8}{8} + \frac{3}{8}$

Combine $9$ and $\frac{8}{8}$ .

$\frac{25 x}{4} = \frac{9 \cdot 8}{8} + \frac{3}{8}$

Combine the numerators over the common denominator.

$\frac{25 x}{4} = \frac{9 \cdot 8 + 3}{8}$

Simplify the numerator.

Multiply $9$ by $8$ .

$\frac{25 x}{4} = \frac{72 + 3}{8}$

Add $72$ and $3$ .

$\frac{25 x}{4} = \frac{75}{8}$

Multiply both sides of the equation by $\frac{4}{25}$ .

$\frac{4}{25} \cdot \frac{25 x}{4} = \frac{4}{25} \cdot \frac{75}{8}$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{4}{25} \cdot \frac{25 x}{4}$ .

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4}{25} \cdot \frac{25 x}{4} = \frac{4}{25} \cdot \frac{75}{8}$

Rewrite the expression.

$\frac{1}{25} (25 x) = \frac{4}{25} \cdot \frac{75}{8}$

Cancel the common factor of $25$ .

Factor $25$ out of $25 x$ .

$\frac{1}{25} (25 (x)) = \frac{4}{25} \cdot \frac{75}{8}$

Cancel the common factor.

$\frac{1}{25} (25 x) = \frac{4}{25} \cdot \frac{75}{8}$

Rewrite the expression.

$x = \frac{4}{25} \cdot \frac{75}{8}$

Simplify the right side.

Simplify $\frac{4}{25} \cdot \frac{75}{8}$ .

Cancel the common factor of $4$ .

Factor $4$ out of $8$ .

$x = \frac{4}{25} \cdot \frac{75}{4 (2)}$

Cancel the common factor.

$x = \frac{4}{25} \cdot \frac{75}{4 \cdot 2}$

Rewrite the expression.

$x = \frac{1}{25} \cdot \frac{75}{2}$

Cancel the common factor of $25$ .

Factor $25$ out of $75$ .

$x = \frac{1}{25} \cdot \frac{25 (3)}{2}$

Cancel the common factor.

$x = \frac{1}{25} \cdot \frac{25 \cdot 3}{2}$

Rewrite the expression.

$x = \frac{3}{2}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3}{2}$

Decimal Form:

$x = 1.5$

Mixed Number Form:

$x = 1 \frac{1}{2}$

Solve for x 7 1/4x-x=9 3/8

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