Convert to Set Notation 4/5x-1/4<=7/10x-4/5

$\frac{4}{5} x - \frac{1}{4} \leq \frac{7}{10} x - \frac{4}{5}$

Step 1

Solve $x \leq - \frac{11}{2}$ .

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

$\frac{4 x}{5} - \frac{1}{4} \leq \frac{7}{10} x - \frac{4}{5}$

Combine $\frac{7}{10}$ and $x$ .

$\frac{4 x}{5} - \frac{1}{4} \leq \frac{7 x}{10} - \frac{4}{5}$

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

Subtract $\frac{7 x}{10}$ from both sides of the inequality.

$\frac{4 x}{5} - \frac{1}{4} - \frac{7 x}{10} \leq - \frac{4}{5}$

To write $\frac{4 x}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{4 x}{5} \cdot \frac{2}{2} - \frac{7 x}{10} - \frac{1}{4} \leq - \frac{4}{5}$

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{4 x}{5}$ by $\frac{2}{2}$ .

$\frac{4 x \cdot 2}{5 \cdot 2} - \frac{7 x}{10} - \frac{1}{4} \leq - \frac{4}{5}$

Multiply $5$ by $2$ .

$\frac{4 x \cdot 2}{10} - \frac{7 x}{10} - \frac{1}{4} \leq - \frac{4}{5}$

Combine the numerators over the common denominator.

$\frac{4 x \cdot 2 - 7 x}{10} - \frac{1}{4} \leq - \frac{4}{5}$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $4 x \cdot 2 - 7 x$ .

Factor $x$ out of $4 x \cdot 2$ .

$\frac{x (4 \cdot 2) - 7 x}{10} - \frac{1}{4} \leq - \frac{4}{5}$

Factor $x$ out of $- 7 x$ .

$\frac{x (4 \cdot 2) + x \cdot - 7}{10} - \frac{1}{4} \leq - \frac{4}{5}$

Factor $x$ out of $x (4 \cdot 2) + x \cdot - 7$ .

$\frac{x (4 \cdot 2 - 7)}{10} - \frac{1}{4} \leq - \frac{4}{5}$

Multiply $4$ by $2$ .

$\frac{x (8 - 7)}{10} - \frac{1}{4} \leq - \frac{4}{5}$

Subtract $7$ from $8$ .

$\frac{x \cdot 1}{10} - \frac{1}{4} \leq - \frac{4}{5}$

Multiply $x$ by $1$ .

$\frac{x}{10} - \frac{1}{4} \leq - \frac{4}{5}$

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

Add $\frac{1}{4}$ to both sides of the inequality.

$\frac{x}{10} \leq - \frac{4}{5} + \frac{1}{4}$

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

$\frac{x}{10} \leq - \frac{4}{5} \cdot \frac{4}{4} + \frac{1}{4}$

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

$\frac{x}{10} \leq - \frac{4}{5} \cdot \frac{4}{4} + \frac{1}{4} \cdot \frac{5}{5}$

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

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

$\frac{x}{10} \leq - \frac{4 \cdot 4}{5 \cdot 4} + \frac{1}{4} \cdot \frac{5}{5}$

Multiply $5$ by $4$ .

$\frac{x}{10} \leq - \frac{4 \cdot 4}{20} + \frac{1}{4} \cdot \frac{5}{5}$

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

$\frac{x}{10} \leq - \frac{4 \cdot 4}{20} + \frac{5}{4 \cdot 5}$

Multiply $4$ by $5$ .

$\frac{x}{10} \leq - \frac{4 \cdot 4}{20} + \frac{5}{20}$

Combine the numerators over the common denominator.

$\frac{x}{10} \leq \frac{- 4 \cdot 4 + 5}{20}$

Simplify the numerator.

Multiply $- 4$ by $4$ .

$\frac{x}{10} \leq \frac{- 16 + 5}{20}$

Add $- 16$ and $5$ .

$\frac{x}{10} \leq \frac{- 11}{20}$

Move the negative in front of the fraction.

$\frac{x}{10} \leq - \frac{11}{20}$

Multiply both sides by $10$ .

$\frac{x}{10} \cdot 10 \leq - \frac{11}{20} \cdot 10$

Simplify.

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{x}{10} \cdot 10 \leq - \frac{11}{20} \cdot 10$

Rewrite the expression.

$x \leq - \frac{11}{20} \cdot 10$

Simplify the right side.

Simplify $- \frac{11}{20} \cdot 10$ .

Cancel the common factor of $10$ .

Move the leading negative in $- \frac{11}{20}$ into the numerator.

$x \leq \frac{- 11}{20} \cdot 10$

Factor $10$ out of $20$ .

$x \leq \frac{- 11}{10 (2)} \cdot 10$

Cancel the common factor.

$x \leq \frac{- 11}{10 \cdot 2} \cdot 10$

Rewrite the expression.

$x \leq \frac{- 11}{2}$

Move the negative in front of the fraction.

$x \leq - \frac{11}{2}$

Step 2

Use the inequality $x \leq - \frac{11}{2}$ to build the set notation.

${x | x \leq - \frac{11}{2}}$

Step 3

Convert to Set Notation 4/5x-1/4<=7/10x-4/5

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