Algebra Examples

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

Step 1

Multiply both sides by $5$ .

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

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

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

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

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $5$ .

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Step 2.2.1.1

Cancel the common factor.

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

Step 2.2.1.2

Rewrite the expression.

$5 x \leq 5 x + 1$

Step 3

Solve for $x$ .

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Step 3.1

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

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Step 3.1.1

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

$5 x - 5 x \leq 1$

Step 3.1.2

Subtract $5 x$ from $5 x$ .

$0 \leq 1$

Step 3.2

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:

$(- \infty, \infty)$