Algebra Examples

$\frac{x}{2} + 1 \leq \frac{5}{2}$

Step 1

Solve $x \leq 3$ .

Tap for more steps...

Step 1.1

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

Tap for more steps...

Step 1.1.1

Subtract $1$ from both sides of the inequality.

$\frac{x}{2} \leq \frac{5}{2} - 1$

Step 1.1.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{x}{2} \leq \frac{5}{2} - 1 \cdot \frac{2}{2}$

Step 1.1.3

Combine $- 1$ and $\frac{2}{2}$ .

$\frac{x}{2} \leq \frac{5}{2} + \frac{- 1 \cdot 2}{2}$

Step 1.1.4

Combine the numerators over the common denominator.

$\frac{x}{2} \leq \frac{5 - 1 \cdot 2}{2}$

Step 1.1.5

Simplify the numerator.

Tap for more steps...

Step 1.1.5.1

Multiply $- 1$ by $2$ .

$\frac{x}{2} \leq \frac{5 - 2}{2}$

Step 1.1.5.2

Subtract $2$ from $5$ .

$\frac{x}{2} \leq \frac{3}{2}$

Step 1.2

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$x \leq 3$

Step 2

Use the inequality $x \leq 3$ to build the set notation.

${x | x \leq 3}$

Step 3