Convert to Interval Notation x/4-3/20

$\frac{x}{4} - \frac{3}{20} \leq \frac{x}{5} + 1$

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

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

$\frac{x}{4} - \frac{3}{20} - \frac{x}{5} \leq 1$

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

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

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

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

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

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

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

Multiply $4$ by $5$ .

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

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

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

Multiply $5$ by $4$ .

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

Combine the numerators over the common denominator.

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

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Move $5$ to the left of $x$ .

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

Multiply $4$ by $- 1$ .

$\frac{5 x - 4 x - 3}{20} \leq 1$

Subtract $4 x$ from $5 x$ .

$\frac{x - 3}{20} \leq 1$

Multiply both sides of the equation by $20$ .

$x - 3 \leq 1 \cdot (20)$

Remove parentheses.

$x - 3 \leq 1 \cdot (20)$

Multiply $20$ by $1$ .

$x - 3 \leq 20$

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

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Add $3$ to both sides of the inequality.

$x \leq 20 + 3$

Add $20$ and $3$ .

$x \leq 23$

Convert the inequality to interval notation.

$(- \infty, 23]$

Convert to Interval Notation x/4-3/20<=x/5+1

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