Solve the Inequality for x x/4>=1-x/8

$\frac{x}{4} \geq 1 - \frac{x}{8}$

Multiply both sides by $4$ .

$\frac{x}{4} \cdot 4 \geq (1 - \frac{x}{8}) \cdot 4$

Simplify.

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{x}{4} \cdot 4 \geq (1 - \frac{x}{8}) \cdot 4$

Rewrite the expression.

$x \geq (1 - \frac{x}{8}) \cdot 4$

Simplify the right side.

Simplify $(1 - \frac{x}{8}) \cdot 4$ .

Apply the distributive property.

$x \geq 1 \cdot 4 - \frac{x}{8} \cdot 4$

Multiply $4$ by $1$ .

$x \geq 4 - \frac{x}{8} \cdot 4$

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{x}{8}$ into the numerator.

$x \geq 4 + \frac{- x}{8} \cdot 4$

Factor $4$ out of $8$ .

$x \geq 4 + \frac{- x}{4 (2)} \cdot 4$

Cancel the common factor.

$x \geq 4 + \frac{- x}{4 \cdot 2} \cdot 4$

Rewrite the expression.

$x \geq 4 + \frac{- x}{2}$

Simplify the expression.

Move the negative in front of the fraction.

$x \geq 4 - \frac{x}{2}$

Reorder $4$ and $- \frac{x}{2}$ .

$x \geq - \frac{x}{2} + 4$

Solve for $x$ .

Move all terms containing $x$ to the left side of the inequality.

Add $\frac{x}{2}$ to both sides of the inequality.

$x + \frac{x}{2} \geq 4$

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

$x \cdot \frac{2}{2} + \frac{x}{2} \geq 4$

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

$\frac{x \cdot 2}{2} + \frac{x}{2} \geq 4$

Combine the numerators over the common denominator.

$\frac{x \cdot 2 + x}{2} \geq 4$

Simplify the numerator.

Move $2$ to the left of $x$ .

$\frac{2 \cdot x + x}{2} \geq 4$

Add $2 x$ and $x$ .

$\frac{3 x}{2} \geq 4$

Multiply both sides by $2$ .

$\frac{3 x}{2} \cdot 2 \geq 4 \cdot 2$

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{3 x}{2} \cdot 2 \geq 4 \cdot 2$

Rewrite the expression.

$3 x \geq 4 \cdot 2$

Simplify the right side.

Multiply $4$ by $2$ .

$3 x \geq 8$

Divide each term in $3 x \geq 8$ by $3$ and simplify.

Divide each term in $3 x \geq 8$ by $3$ .

$\frac{3 x}{3} \geq \frac{8}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} \geq \frac{8}{3}$

Divide $x$ by $1$ .

$x \geq \frac{8}{3}$

The result can be shown in multiple forms.

Inequality Form:

$x \geq \frac{8}{3}$

Interval Notation:

$[\frac{8}{3}, \infty)$

Solve the Inequality for x x/4>=1-x/8

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