Solve for x -3/5x+1/5>7/20

$- \frac{3}{5} x + \frac{1}{5} > \frac{7}{20}$

Step 1

Simplify each term.

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

$- \frac{x \cdot 3}{5} + \frac{1}{5} > \frac{7}{20}$

Move $3$ to the left of $x$ .

$- \frac{3 x}{5} + \frac{1}{5} > \frac{7}{20}$

Step 2

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

Subtract $\frac{1}{5}$ from both sides of the inequality.

$- \frac{3 x}{5} > \frac{7}{20} - \frac{1}{5}$

To write $- \frac{1}{5}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{3 x}{5} > \frac{7}{20} - \frac{1}{5} \cdot \frac{4}{4}$

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{5}$ by $\frac{4}{4}$ .

$- \frac{3 x}{5} > \frac{7}{20} - \frac{4}{5 \cdot 4}$

Multiply $5$ by $4$ .

$- \frac{3 x}{5} > \frac{7}{20} - \frac{4}{20}$

Combine the numerators over the common denominator.

$- \frac{3 x}{5} > \frac{7 - 4}{20}$

Subtract $4$ from $7$ .

$- \frac{3 x}{5} > \frac{3}{20}$

Step 3

Divide each term in $- \frac{3 x}{5} > \frac{3}{20}$ by $- 1$ and simplify.

Divide each term in $- \frac{3 x}{5} > \frac{3}{20}$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{3 x}{5}}{- 1} < \frac{\frac{3}{20}}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{\frac{3 x}{5}}{1} < \frac{\frac{3}{20}}{- 1}$

Divide $\frac{3 x}{5}$ by $1$ .

$\frac{3 x}{5} < \frac{\frac{3}{20}}{- 1}$

Simplify the right side.

Move the negative one from the denominator of $\frac{\frac{3}{20}}{- 1}$ .

$\frac{3 x}{5} < - 1 \cdot \frac{3}{20}$

Rewrite $- 1 \cdot \frac{3}{20}$ as $- \frac{3}{20}$ .

$\frac{3 x}{5} < - \frac{3}{20}$

Step 4

Multiply both sides by $5$ .

$\frac{3 x}{5} \cdot 5 < - \frac{3}{20} \cdot 5$

Step 5

Simplify.

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{3 x}{5} \cdot 5 < - \frac{3}{20} \cdot 5$

Rewrite the expression.

$3 x < - \frac{3}{20} \cdot 5$

Simplify the right side.

Simplify $- \frac{3}{20} \cdot 5$ .

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{3}{20}$ into the numerator.

$3 x < \frac{- 3}{20} \cdot 5$

Factor $5$ out of $20$ .

$3 x < \frac{- 3}{5 (4)} \cdot 5$

Cancel the common factor.

$3 x < \frac{- 3}{5 \cdot 4} \cdot 5$

Rewrite the expression.

$3 x < \frac{- 3}{4}$

Move the negative in front of the fraction.

$3 x < - \frac{3}{4}$

Step 6

Divide each term in $3 x < - \frac{3}{4}$ by $3$ and simplify.

Divide each term in $3 x < - \frac{3}{4}$ by $3$ .

$\frac{3 x}{3} < \frac{- \frac{3}{4}}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} < \frac{- \frac{3}{4}}{3}$

Divide $x$ by $1$ .

$x < \frac{- \frac{3}{4}}{3}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$x < - \frac{3}{4} \cdot \frac{1}{3}$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$x < \frac{- 3}{4} \cdot \frac{1}{3}$

Factor $3$ out of $- 3$ .

$x < \frac{3 (- 1)}{4} \cdot \frac{1}{3}$

Cancel the common factor.

$x < \frac{3 \cdot - 1}{4} \cdot \frac{1}{3}$

Rewrite the expression.

$x < \frac{- 1}{4}$

Move the negative in front of the fraction.

$x < - \frac{1}{4}$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$x < - \frac{1}{4}$

Interval Notation:

$(- \infty, - \frac{1}{4})$

Solve for x -3/5x+1/5>7/20

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