Solve the Inequality for x 3/4x+1/2<=5/4

$\frac{3}{4} x + \frac{1}{2} \leq \frac{5}{4}$

Step 1

Combine $\frac{3}{4}$ and $x$ .

$\frac{3 x}{4} + \frac{1}{2} \leq \frac{5}{4}$

Step 2

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

Subtract $\frac{1}{2}$ from both sides of the inequality.

$\frac{3 x}{4} \leq \frac{5}{4} - \frac{1}{2}$

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

$\frac{3 x}{4} \leq \frac{5}{4} - \frac{1}{2} \cdot \frac{2}{2}$

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{2}$ by $\frac{2}{2}$ .

$\frac{3 x}{4} \leq \frac{5}{4} - \frac{2}{2 \cdot 2}$

Multiply $2$ by $2$ .

$\frac{3 x}{4} \leq \frac{5}{4} - \frac{2}{4}$

Combine the numerators over the common denominator.

$\frac{3 x}{4} \leq \frac{5 - 2}{4}$

Subtract $2$ from $5$ .

$\frac{3 x}{4} \leq \frac{3}{4}$

Step 3

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

$3 x \leq 3$

Step 4

Divide each term in $3 x \leq 3$ by $3$ and simplify.

Divide each term in $3 x \leq 3$ by $3$ .

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $3$ by $3$ .

$x \leq 1$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x \leq 1$

Interval Notation:

$(- \infty, 1]$