Solve for x 8(x/4-6)>=4

$8 (\frac{x}{4} - 6) \geq 4$

Simplify.

Apply the distributive property.

$8 \frac{x}{4} + 8 \cdot - 6 \geq 4$

Cancel the common factor of $4$ .

Factor $4$ out of $8$ .

$4 (2) \frac{x}{4} + 8 \cdot - 6 \geq 4$

Cancel the common factor.

$4 \cdot 2 \frac{x}{4} + 8 \cdot - 6 \geq 4$

Rewrite the expression.

$2 x + 8 \cdot - 6 \geq 4$

Multiply $8$ by $- 6$ .

$2 x - 48 \geq 4$

Divide each term in $(2 x - 48) \geq 4$ by $8$ and simplify.

Divide each term in $(2 x - 48) \geq 4$ by $8$ .

$\frac{(2 x - 48)}{8} \geq \frac{4}{8}$

Simplify the left side.

Cancel the common factor of $2 x - 48$ and $8$ .

Factor $2$ out of $2 x$ .

$\frac{2 (x) - 48}{8} \geq \frac{4}{8}$

Factor $2$ out of $- 48$ .

$\frac{2 x + 2 \cdot - 24}{8} \geq \frac{4}{8}$

Factor $2$ out of $2 x + 2 \cdot - 24$ .

$\frac{2 (x - 24)}{8} \geq \frac{4}{8}$

Cancel the common factors.

Factor $2$ out of $8$ .

$\frac{2 (x - 24)}{2 (4)} \geq \frac{4}{8}$

Cancel the common factor.

$\frac{2 (x - 24)}{2 \cdot 4} \geq \frac{4}{8}$

Rewrite the expression.

$\frac{x - 24}{4} \geq \frac{4}{8}$

Simplify the right side.

Cancel the common factor of $4$ and $8$ .

Factor $4$ out of $4$ .

$\frac{x - 24}{4} \geq \frac{4 (1)}{8}$

Cancel the common factors.

Factor $4$ out of $8$ .

$\frac{x - 24}{4} \geq \frac{4 \cdot 1}{4 \cdot 2}$

Cancel the common factor.

$\frac{x - 24}{4} \geq \frac{4 \cdot 1}{4 \cdot 2}$

Rewrite the expression.

$\frac{x - 24}{4} \geq \frac{1}{2}$

Multiply both sides by $4$ .

$\frac{x - 24}{4} \cdot 4 \geq \frac{1}{2} \cdot 4$

Simplify.

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{x - 24}{4} \cdot 4 \geq \frac{1}{2} \cdot 4$

Rewrite the expression.

$x - 24 \geq \frac{1}{2} \cdot 4$

Simplify the right side.

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$x - 24 \geq \frac{1}{2} \cdot (2 (2))$

Cancel the common factor.

$x - 24 \geq \frac{1}{2} \cdot (2 \cdot 2)$

Rewrite the expression.

$x - 24 \geq 2$

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

Add $24$ to both sides of the inequality.

$x \geq 2 + 24$

Add $2$ and $24$ .

$x \geq 26$

The result can be shown in multiple forms.

Inequality Form:

$x \geq 26$

Interval Notation:

$[26, \infty)$

Solve for x 8(x/4-6)>=4

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