Solve the Inequality for x 3(8-4x)<6(x-5)

$3 (8 - 4 x) < 6 (x - 5)$

Step 1

Simplify $3 (8 - 4 x)$ .

Start simplifying.

$0 + 0 + 3 (8 - 4 x) < 6 (x - 5)$

Simplify by adding zeros.

$3 (8 - 4 x) < 6 (x - 5)$

Apply the distributive property.

$3 \cdot 8 + 3 (- 4 x) < 6 (x - 5)$

Multiply.

Multiply $3$ by $8$ .

$24 + 3 (- 4 x) < 6 (x - 5)$

Multiply $- 4$ by $3$ .

$24 - 12 x < 6 (x - 5)$

Step 2

Simplify $6 (x - 5)$ .

Apply the distributive property.

$24 - 12 x < 6 x + 6 \cdot - 5$

Multiply $6$ by $- 5$ .

$24 - 12 x < 6 x - 30$

Step 3

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

Subtract $6 x$ from both sides of the inequality.

$24 - 12 x - 6 x < - 30$

Subtract $6 x$ from $- 12 x$ .

$24 - 18 x < - 30$

Step 4

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

Subtract $24$ from both sides of the inequality.

$- 18 x < - 30 - 24$

Subtract $24$ from $- 30$ .

$- 18 x < - 54$

Step 5

Divide each term in $- 18 x < - 54$ by $- 18$ and simplify.

Divide each term in $- 18 x < - 54$ by $- 18$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 18 x}{- 18} > \frac{- 54}{- 18}$

Simplify the left side.

Cancel the common factor of $- 18$ .

Cancel the common factor.

$\frac{- 18 x}{- 18} > \frac{- 54}{- 18}$

Divide $x$ by $1$ .

$x > \frac{- 54}{- 18}$

Simplify the right side.

Divide $- 54$ by $- 18$ .

$x > 3$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x > 3$

Interval Notation:

$(3, \infty)$

Solve the Inequality for x 3(8-4x)<6(x-5)

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