Solve the Inequality for x x<=(5x+1)/5

$x \leq \frac{5 x + 1}{5}$

Step 1

Multiply both sides by $5$ .

$x \cdot 5 \leq \frac{5 x + 1}{5} \cdot 5$

Step 2

Simplify.

Simplify the left side.

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

$5 x \leq \frac{5 x + 1}{5} \cdot 5$

Simplify the right side.

Cancel the common factor of $5$ .

Cancel the common factor.

$5 x \leq \frac{5 x + 1}{5} \cdot 5$

Rewrite the expression.

$5 x \leq 5 x + 1$

Step 3

Solve for $x$ .

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

Subtract $5 x$ from both sides of the inequality.

$5 x - 5 x \leq 1$

Subtract $5 x$ from $5 x$ .

$0 \leq 1$

Since $0 \leq 1$ , the inequality will always be true.

Always true

Step 4

The result can be shown in multiple forms.

Always true

Interval Notation:

$(- \infty, \infty)$