Solve for x 1/4x-2<-1 1/2

$\frac{1}{4} x - 2 < - 1 \frac{1}{2}$

Step 1

Simplify the left side.

Combine $\frac{1}{4}$ and $x$ .

$\frac{x}{4} - 2 < - 1 \frac{1}{2}$

Step 2

Simplify the right side.

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

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

$\frac{x}{4} - 2 < - (1 + \frac{1}{2})$

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

Write $1$ as a fraction with a common denominator.

$\frac{x}{4} - 2 < - (\frac{2}{2} + \frac{1}{2})$

Combine the numerators over the common denominator.

$\frac{x}{4} - 2 < - \frac{2 + 1}{2}$

Add $2$ and $1$ .

$\frac{x}{4} - 2 < - \frac{3}{2}$

Step 3

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

Add $2$ to both sides of the inequality.

$\frac{x}{4} < - \frac{3}{2} + 2$

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

$\frac{x}{4} < - \frac{3}{2} + 2 \cdot \frac{2}{2}$

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

$\frac{x}{4} < - \frac{3}{2} + \frac{2 \cdot 2}{2}$

Combine the numerators over the common denominator.

$\frac{x}{4} < \frac{- 3 + 2 \cdot 2}{2}$

Simplify the numerator.

Multiply $2$ by $2$ .

$\frac{x}{4} < \frac{- 3 + 4}{2}$

Add $- 3$ and $4$ .

$\frac{x}{4} < \frac{1}{2}$

Step 4

Multiply both sides by $4$ .

$\frac{x}{4} \cdot 4 < \frac{1}{2} \cdot 4$

Step 5

Simplify.

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{x}{4} \cdot 4 < \frac{1}{2} \cdot 4$

Rewrite the expression.

$x < \frac{1}{2} \cdot 4$

Simplify the right side.

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$x < \frac{1}{2} \cdot (2 (2))$

Cancel the common factor.

$x < \frac{1}{2} \cdot (2 \cdot 2)$

Rewrite the expression.

$x < 2$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x < 2$

Interval Notation:

$(- \infty, 2)$

Step 7

Solve for x 1/4x-2<-1 1/2

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