Solve the Inequality for x 4 1/2<=1.2x

$4 \frac{1}{2} \leq 1.2 x$

Simplify the left side.

Convert $4 \frac{1}{2}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$4 + \frac{1}{2} \leq 1.2 x$

Add $4$ and $\frac{1}{2}$ .

To write $4$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$4 \cdot \frac{2}{2} + \frac{1}{2} \leq 1.2 x$

Combine $4$ and $\frac{2}{2}$ .

$\frac{4 \cdot 2}{2} + \frac{1}{2} \leq 1.2 x$

Combine the numerators over the common denominator.

$\frac{4 \cdot 2 + 1}{2} \leq 1.2 x$

Simplify the numerator.

Multiply $4$ by $2$ .

$\frac{8 + 1}{2} \leq 1.2 x$

Add $8$ and $1$ .

$\frac{9}{2} \leq 1.2 x$

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

$1.2 x \geq \frac{9}{2}$

Divide each term in $1.2 x \geq \frac{9}{2}$ by $1.2$ and simplify.

Divide each term in $1.2 x \geq \frac{9}{2}$ by $1.2$ .

$\frac{1.2 x}{1.2} \geq \frac{\frac{9}{2}}{1.2}$

Simplify the left side.

Cancel the common factor of $1.2$ .

Cancel the common factor.

$\frac{1.2 x}{1.2} \geq \frac{\frac{9}{2}}{1.2}$

Divide $x$ by $1$ .

$x \geq \frac{\frac{9}{2}}{1.2}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$x \geq \frac{9}{2} \cdot \frac{1}{1.2}$

Divide $1$ by $1.2$ .

$x \geq \frac{9}{2} \cdot 0.8\overline{3}$

Multiply $\frac{9}{2} \cdot 0.8\overline{3}$ .

Combine $\frac{9}{2}$ and $0.8\overline{3}$ .

$x \geq \frac{9 \cdot 0.8\overline{3}}{2}$

Multiply $9$ by $0.8\overline{3}$ .

$x \geq \frac{7.4\overline{9}}{2}$

Divide $7.4\overline{9}$ by $2$ .

$x \geq 3.74\overline{9}$

The result can be shown in multiple forms.

Inequality Form:

$x \geq 3.74\overline{9}$

Interval Notation:

$[3.74\overline{9}, \infty)$