Solve the Inequality for m m/4-3/20<=m/5+1

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

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

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

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

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

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

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

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

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

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

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

Multiply $4$ by $5$ .

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

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

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

Multiply $5$ by $4$ .

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

Combine the numerators over the common denominator.

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

Combine the numerators over the common denominator.

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

Simplify each term.

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

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

Multiply $4$ by $- 1$ .

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

Subtract $4 m$ from $5 m$ .

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

Multiply both sides by $20$ .

$\frac{m - 3}{20} \cdot 20 \leq 1 \cdot 20$

Simplify.

Simplify the left side.

Cancel the common factor of $20$ .

Cancel the common factor.

$\frac{m - 3}{20} \cdot 20 \leq 1 \cdot 20$

Rewrite the expression.

$m - 3 \leq 1 \cdot 20$

Simplify the right side.

Multiply $20$ by $1$ .

$m - 3 \leq 20$

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

Add $3$ to both sides of the inequality.

$m \leq 20 + 3$

Add $20$ and $3$ .

$m \leq 23$

The result can be shown in multiple forms.

Inequality Form:

$m \leq 23$

Interval Notation:

$(- \infty, 23]$

Solve the Inequality for m m/4-3/20<=m/5+1

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