Solve the Inequality for x 8(1/4x-3)+24<4(x+5)

$8 (\frac{1}{4} x - 3) + 24 < 4 (x + 5)$

Step 1

Simplify $8 (\frac{1}{4} x - 3) + 24$ .

Simplify each term.

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

$8 (\frac{x}{4} - 3) + 24 < 4 (x + 5)$

Apply the distributive property.

$8 \frac{x}{4} + 8 \cdot - 3 + 24 < 4 (x + 5)$

Cancel the common factor of $4$ .

Factor $4$ out of $8$ .

$4 (2) \frac{x}{4} + 8 \cdot - 3 + 24 < 4 (x + 5)$

Cancel the common factor.

$4 \cdot 2 \frac{x}{4} + 8 \cdot - 3 + 24 < 4 (x + 5)$

Rewrite the expression.

$2 x + 8 \cdot - 3 + 24 < 4 (x + 5)$

Multiply $8$ by $- 3$ .

$2 x - 24 + 24 < 4 (x + 5)$

Combine the opposite terms in $2 x - 24 + 24$ .

Add $- 24$ and $24$ .

$2 x + 0 < 4 (x + 5)$

Add $2 x$ and $0$ .

$2 x < 4 (x + 5)$

Step 2

Simplify $4 (x + 5)$ .

Apply the distributive property.

$2 x < 4 x + 4 \cdot 5$

Multiply $4$ by $5$ .

$2 x < 4 x + 20$

Step 3

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

Subtract $4 x$ from both sides of the inequality.

$2 x - 4 x < 20$

Subtract $4 x$ from $2 x$ .

$- 2 x < 20$

Step 4

Divide each term in $- 2 x < 20$ by $- 2$ and simplify.

Divide each term in $- 2 x < 20$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 x}{- 2} > \frac{20}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} > \frac{20}{- 2}$

Divide $x$ by $1$ .

$x > \frac{20}{- 2}$

Simplify the right side.

Divide $20$ by $- 2$ .

$x > - 10$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x > - 10$

Interval Notation:

$(- 10, \infty)$

Solve the Inequality for x 8(1/4x-3)+24<4(x+5)

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