Solve the Inequality for x 4>=x+3/4

$4 \geq x + \frac{3}{4}$

Rewrite so $x$ is on the left side of the inequality.

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

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

Subtract $\frac{3}{4}$ from both sides of the inequality.

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $4$ by $4$ .

$x \leq \frac{16 - 3}{4}$

Subtract $3$ from $16$ .

$x \leq \frac{13}{4}$

The result can be shown in multiple forms.

Inequality Form:

$x \leq \frac{13}{4}$

Interval Notation:

$(- \infty, \frac{13}{4}]$