Solve for x 4/5(x-3/10)=-2 1/4

$\frac{4}{5} (x - \frac{3}{10}) = - 2 \frac{1}{4}$

Step 1

Simplify the left side.

Simplify $\frac{4}{5} \cdot (x - \frac{3}{10})$ .

Apply the distributive property.

$\frac{4}{5} x + \frac{4}{5} (- \frac{3}{10}) = - 2 \frac{1}{4}$

Combine $\frac{4}{5}$ and $x$ .

$\frac{4 x}{5} + \frac{4}{5} (- \frac{3}{10}) = - 2 \frac{1}{4}$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{3}{10}$ into the numerator.

$\frac{4 x}{5} + \frac{4}{5} \cdot \frac{- 3}{10} = - 2 \frac{1}{4}$

Factor $2$ out of $4$ .

$\frac{4 x}{5} + \frac{2 (2)}{5} \cdot \frac{- 3}{10} = - 2 \frac{1}{4}$

Factor $2$ out of $10$ .

$\frac{4 x}{5} + \frac{2 \cdot 2}{5} \cdot \frac{- 3}{2 \cdot 5} = - 2 \frac{1}{4}$

Cancel the common factor.

$\frac{4 x}{5} + \frac{2 \cdot 2}{5} \cdot \frac{- 3}{2 \cdot 5} = - 2 \frac{1}{4}$

Rewrite the expression.

$\frac{4 x}{5} + \frac{2}{5} \cdot \frac{- 3}{5} = - 2 \frac{1}{4}$

Multiply $\frac{2}{5}$ by $\frac{- 3}{5}$ .

$\frac{4 x}{5} + \frac{2 \cdot - 3}{5 \cdot 5} = - 2 \frac{1}{4}$

Simplify the expression.

Multiply $2$ by $- 3$ .

$\frac{4 x}{5} + \frac{- 6}{5 \cdot 5} = - 2 \frac{1}{4}$

Multiply $5$ by $5$ .

$\frac{4 x}{5} + \frac{- 6}{25} = - 2 \frac{1}{4}$

Move the negative in front of the fraction.

$\frac{4 x}{5} - \frac{6}{25} = - 2 \frac{1}{4}$

Step 2

Simplify the right side.

Convert $2 \frac{1}{4}$ to an improper fraction.

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

$\frac{4 x}{5} - \frac{6}{25} = - (2 + \frac{1}{4})$

Add $2$ and $\frac{1}{4}$ .

To write $2$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{4 x}{5} - \frac{6}{25} = - (2 \cdot \frac{4}{4} + \frac{1}{4})$

Combine $2$ and $\frac{4}{4}$ .

$\frac{4 x}{5} - \frac{6}{25} = - (\frac{2 \cdot 4}{4} + \frac{1}{4})$

Combine the numerators over the common denominator.

$\frac{4 x}{5} - \frac{6}{25} = - \frac{2 \cdot 4 + 1}{4}$

Simplify the numerator.

Multiply $2$ by $4$ .

$\frac{4 x}{5} - \frac{6}{25} = - \frac{8 + 1}{4}$

Add $8$ and $1$ .

$\frac{4 x}{5} - \frac{6}{25} = - \frac{9}{4}$

Step 3

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

Add $\frac{6}{25}$ to both sides of the equation.

$\frac{4 x}{5} = - \frac{9}{4} + \frac{6}{25}$

To write $- \frac{9}{4}$ as a fraction with a common denominator, multiply by $\frac{25}{25}$ .

$\frac{4 x}{5} = - \frac{9}{4} \cdot \frac{25}{25} + \frac{6}{25}$

To write $\frac{6}{25}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{4 x}{5} = - \frac{9}{4} \cdot \frac{25}{25} + \frac{6}{25} \cdot \frac{4}{4}$

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

Multiply $\frac{9}{4}$ by $\frac{25}{25}$ .

$\frac{4 x}{5} = - \frac{9 \cdot 25}{4 \cdot 25} + \frac{6}{25} \cdot \frac{4}{4}$

Multiply $4$ by $25$ .

$\frac{4 x}{5} = - \frac{9 \cdot 25}{100} + \frac{6}{25} \cdot \frac{4}{4}$

Multiply $\frac{6}{25}$ by $\frac{4}{4}$ .

$\frac{4 x}{5} = - \frac{9 \cdot 25}{100} + \frac{6 \cdot 4}{25 \cdot 4}$

Multiply $25$ by $4$ .

$\frac{4 x}{5} = - \frac{9 \cdot 25}{100} + \frac{6 \cdot 4}{100}$

Combine the numerators over the common denominator.

$\frac{4 x}{5} = \frac{- 9 \cdot 25 + 6 \cdot 4}{100}$

Simplify the numerator.

Multiply $- 9$ by $25$ .

$\frac{4 x}{5} = \frac{- 225 + 6 \cdot 4}{100}$

Multiply $6$ by $4$ .

$\frac{4 x}{5} = \frac{- 225 + 24}{100}$

Add $- 225$ and $24$ .

$\frac{4 x}{5} = \frac{- 201}{100}$

Move the negative in front of the fraction.

$\frac{4 x}{5} = - \frac{201}{100}$

Step 4

Multiply both sides of the equation by $\frac{5}{4}$ .

$\frac{5}{4} \cdot \frac{4 x}{5} = \frac{5}{4} (- \frac{201}{100})$

Step 5

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{5}{4} \cdot \frac{4 x}{5}$ .

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5}{4} \cdot \frac{4 x}{5} = \frac{5}{4} (- \frac{201}{100})$

Rewrite the expression.

$\frac{1}{4} (4 x) = \frac{5}{4} (- \frac{201}{100})$

Cancel the common factor of $4$ .

Factor $4$ out of $4 x$ .

$\frac{1}{4} (4 (x)) = \frac{5}{4} (- \frac{201}{100})$

Cancel the common factor.

$\frac{1}{4} (4 x) = \frac{5}{4} (- \frac{201}{100})$

Rewrite the expression.

$x = \frac{5}{4} (- \frac{201}{100})$

Simplify the right side.

Simplify $\frac{5}{4} (- \frac{201}{100})$ .

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{201}{100}$ into the numerator.

$x = \frac{5}{4} \cdot \frac{- 201}{100}$

Factor $5$ out of $100$ .

$x = \frac{5}{4} \cdot \frac{- 201}{5 (20)}$

Cancel the common factor.

$x = \frac{5}{4} \cdot \frac{- 201}{5 \cdot 20}$

Rewrite the expression.

$x = \frac{1}{4} \cdot \frac{- 201}{20}$

Multiply $\frac{1}{4}$ by $\frac{- 201}{20}$ .

$x = \frac{- 201}{4 \cdot 20}$

Simplify the expression.

Multiply $4$ by $20$ .

$x = \frac{- 201}{80}$

Move the negative in front of the fraction.

$x = - \frac{201}{80}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{201}{80}$

Decimal Form:

$x = - 2.5125$

Mixed Number Form:

$x = - 2 \frac{41}{80}$

Solve for x 4/5(x-3/10)=-2 1/4

Related Questions

Support LCMGCF.com by disabling your adblocker.