Solve the Inequality for x x/4-1/10<=x/5+1

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

Step 1

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

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

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

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

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

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

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

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

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

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

Multiply $4$ by $5$ .

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

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

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

Multiply $5$ by $4$ .

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

Combine the numerators over the common denominator.

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

Simplify each term.

Simplify the numerator.

Factor $x$ out of $x \cdot 5 - x \cdot 4$ .

Factor $x$ out of $x \cdot 5$ .

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

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

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

Factor $x$ out of $x (5) + x (- 1 \cdot 4)$ .

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

Multiply $- 1$ by $4$ .

$\frac{x (5 - 4)}{20} - \frac{1}{10} \leq 1$

Subtract $4$ from $5$ .

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

Multiply $x$ by $1$ .

$\frac{x}{20} - \frac{1}{10} \leq 1$

Step 2

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

Add $\frac{1}{10}$ to both sides of the inequality.

$\frac{x}{20} \leq 1 + \frac{1}{10}$

Write $1$ as a fraction with a common denominator.

$\frac{x}{20} \leq \frac{10}{10} + \frac{1}{10}$

Combine the numerators over the common denominator.

$\frac{x}{20} \leq \frac{10 + 1}{10}$

Add $10$ and $1$ .

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

Step 3

Multiply both sides by $20$ .

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

Step 4

Simplify.

Simplify the left side.

Cancel the common factor of $20$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the right side.

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

Cancel the common factor of $10$ .

Factor $10$ out of $20$ .

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

Cancel the common factor.

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

Rewrite the expression.

$x \leq 11 \cdot 2$

Multiply $11$ by $2$ .

$x \leq 22$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x \leq 22$

Interval Notation:

$(- \infty, 22]$

Solve the Inequality for x x/4-1/10<=x/5+1

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