Solve for x 3/5(x-7/10)=-3 1/4

$\frac{3}{5} (x - \frac{7}{10}) = - 3 \frac{1}{4}$

Simplify the left side.

Simplify $\frac{3}{5} \cdot (x - \frac{7}{10})$ .

Apply the distributive property.

$\frac{3}{5} x + \frac{3}{5} (- \frac{7}{10}) = - 3 \frac{1}{4}$

Combine $\frac{3}{5}$ and $x$ .

$\frac{3 x}{5} + \frac{3}{5} (- \frac{7}{10}) = - 3 \frac{1}{4}$

Multiply $\frac{3}{5} (- \frac{7}{10})$ .

Multiply $\frac{3}{5}$ by $\frac{7}{10}$ .

$\frac{3 x}{5} - \frac{3 \cdot 7}{5 \cdot 10} = - 3 \frac{1}{4}$

Multiply $3$ by $7$ .

$\frac{3 x}{5} - \frac{21}{5 \cdot 10} = - 3 \frac{1}{4}$

Multiply $5$ by $10$ .

$\frac{3 x}{5} - \frac{21}{50} = - 3 \frac{1}{4}$

Simplify the right side.

Convert $3 \frac{1}{4}$ to an improper fraction.

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

$\frac{3 x}{5} - \frac{21}{50} = - (3 + \frac{1}{4})$

Add $3$ and $\frac{1}{4}$ .

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

$\frac{3 x}{5} - \frac{21}{50} = - (3 \cdot \frac{4}{4} + \frac{1}{4})$

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

$\frac{3 x}{5} - \frac{21}{50} = - (\frac{3 \cdot 4}{4} + \frac{1}{4})$

Combine the numerators over the common denominator.

$\frac{3 x}{5} - \frac{21}{50} = - \frac{3 \cdot 4 + 1}{4}$

Simplify the numerator.

Multiply $3$ by $4$ .

$\frac{3 x}{5} - \frac{21}{50} = - \frac{12 + 1}{4}$

Add $12$ and $1$ .

$\frac{3 x}{5} - \frac{21}{50} = - \frac{13}{4}$

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

Add $\frac{21}{50}$ to both sides of the equation.

$\frac{3 x}{5} = - \frac{13}{4} + \frac{21}{50}$

To write $- \frac{13}{4}$ as a fraction with a common denominator, multiply by $\frac{25}{25}$ .

$\frac{3 x}{5} = - \frac{13}{4} \cdot \frac{25}{25} + \frac{21}{50}$

To write $\frac{21}{50}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3 x}{5} = - \frac{13}{4} \cdot \frac{25}{25} + \frac{21}{50} \cdot \frac{2}{2}$

Write each expression with a common denominator of $100$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{13}{4}$ by $\frac{25}{25}$ .

$\frac{3 x}{5} = - \frac{13 \cdot 25}{4 \cdot 25} + \frac{21}{50} \cdot \frac{2}{2}$

Multiply $4$ by $25$ .

$\frac{3 x}{5} = - \frac{13 \cdot 25}{100} + \frac{21}{50} \cdot \frac{2}{2}$

Multiply $\frac{21}{50}$ by $\frac{2}{2}$ .

$\frac{3 x}{5} = - \frac{13 \cdot 25}{100} + \frac{21 \cdot 2}{50 \cdot 2}$

Multiply $50$ by $2$ .

$\frac{3 x}{5} = - \frac{13 \cdot 25}{100} + \frac{21 \cdot 2}{100}$

Combine the numerators over the common denominator.

$\frac{3 x}{5} = \frac{- 13 \cdot 25 + 21 \cdot 2}{100}$

Simplify the numerator.

Multiply $- 13$ by $25$ .

$\frac{3 x}{5} = \frac{- 325 + 21 \cdot 2}{100}$

Multiply $21$ by $2$ .

$\frac{3 x}{5} = \frac{- 325 + 42}{100}$

Add $- 325$ and $42$ .

$\frac{3 x}{5} = \frac{- 283}{100}$

Move the negative in front of the fraction.

$\frac{3 x}{5} = - \frac{283}{100}$

Multiply both sides of the equation by $\frac{5}{3}$ .

$\frac{5}{3} \cdot \frac{3 x}{5} = \frac{5}{3} (- \frac{283}{100})$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{5}{3} \cdot \frac{3 x}{5}$ .

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5}{3} \cdot \frac{3 x}{5} = \frac{5}{3} (- \frac{283}{100})$

Rewrite the expression.

$\frac{1}{3} (3 x) = \frac{5}{3} (- \frac{283}{100})$

Cancel the common factor of $3$ .

Factor $3$ out of $3 x$ .

$\frac{1}{3} (3 (x)) = \frac{5}{3} (- \frac{283}{100})$

Cancel the common factor.

$\frac{1}{3} (3 x) = \frac{5}{3} (- \frac{283}{100})$

Rewrite the expression.

$x = \frac{5}{3} (- \frac{283}{100})$

Simplify the right side.

Simplify $\frac{5}{3} (- \frac{283}{100})$ .

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{283}{100}$ into the numerator.

$x = \frac{5}{3} \cdot \frac{- 283}{100}$

Factor $5$ out of $100$ .

$x = \frac{5}{3} \cdot \frac{- 283}{5 (20)}$

Cancel the common factor.

$x = \frac{5}{3} \cdot \frac{- 283}{5 \cdot 20}$

Rewrite the expression.

$x = \frac{1}{3} \cdot \frac{- 283}{20}$

Multiply $\frac{1}{3}$ by $\frac{- 283}{20}$ .

$x = \frac{- 283}{3 \cdot 20}$

Simplify the expression.

Multiply $3$ by $20$ .

$x = \frac{- 283}{60}$

Move the negative in front of the fraction.

$x = - \frac{283}{60}$

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{283}{60}$

Decimal Form:

$x = - 4.71\overline{6}$

Mixed Number Form:

$x = - 4 \frac{43}{60}$

Solve for x 3/5(x-7/10)=-3 1/4

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