Solve the Inequality for x -4(3x-5)<2(3x+4)

$- 4 (3 x - 5) < 2 (3 x + 4)$

Step 1

Simplify $- 4 (3 x - 5)$ .

Start simplifying.

$0 + 0 - 4 (3 x - 5) < 2 (3 x + 4)$

Simplify by adding zeros.

$- 4 (3 x - 5) < 2 (3 x + 4)$

Apply the distributive property.

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

Multiply.

Multiply $3$ by $- 4$ .

$- 12 x - 4 \cdot - 5 < 2 (3 x + 4)$

Multiply $- 4$ by $- 5$ .

$- 12 x + 20 < 2 (3 x + 4)$

Step 2

Simplify $2 (3 x + 4)$ .

Apply the distributive property.

$- 12 x + 20 < 2 (3 x) + 2 \cdot 4$

Multiply.

Multiply $3$ by $2$ .

$- 12 x + 20 < 6 x + 2 \cdot 4$

Multiply $2$ by $4$ .

$- 12 x + 20 < 6 x + 8$

Step 3

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

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

$- 12 x + 20 - 6 x < 8$

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

$- 18 x + 20 < 8$

Step 4

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

Subtract $20$ from both sides of the inequality.

$- 18 x < 8 - 20$

Subtract $20$ from $8$ .

$- 18 x < - 12$

Step 5

Divide each term in $- 18 x < - 12$ by $- 18$ and simplify.

Divide each term in $- 18 x < - 12$ by $- 18$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 18 x}{- 18} > \frac{- 12}{- 18}$

Simplify the left side.

Cancel the common factor of $- 18$ .

Cancel the common factor.

$\frac{- 18 x}{- 18} > \frac{- 12}{- 18}$

Divide $x$ by $1$ .

$x > \frac{- 12}{- 18}$

Simplify the right side.

Cancel the common factor of $- 12$ and $- 18$ .

Factor $- 6$ out of $- 12$ .

$x > \frac{- 6 (2)}{- 18}$

Cancel the common factors.

Factor $- 6$ out of $- 18$ .

$x > \frac{- 6 \cdot 2}{- 6 \cdot 3}$

Cancel the common factor.

$x > \frac{- 6 \cdot 2}{- 6 \cdot 3}$

Rewrite the expression.

$x > \frac{2}{3}$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x > \frac{2}{3}$

Interval Notation:

$(\frac{2}{3}, \infty)$

Solve the Inequality for x -4(3x-5)<2(3x+4)

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