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

$2 (4 x - 3) \geq - 3 (3 x) + 5 x$

Step 1

Rewrite so $x$ is on the left side of the inequality.

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

Step 2

Simplify $- 3 \cdot (3 x) + 5 x$ .

Multiply $3$ by $- 3$ .

$- 9 x + 5 x \leq 2 (4 x - 3)$

Add $- 9 x$ and $5 x$ .

$- 4 x \leq 2 (4 x - 3)$

Step 3

Simplify $2 (4 x - 3)$ .

Apply the distributive property.

$- 4 x \leq 2 (4 x) + 2 \cdot - 3$

Multiply.

Multiply $4$ by $2$ .

$- 4 x \leq 8 x + 2 \cdot - 3$

Multiply $2$ by $- 3$ .

$- 4 x \leq 8 x - 6$

Step 4

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

Subtract $8 x$ from both sides of the inequality.

$- 4 x - 8 x \leq - 6$

Subtract $8 x$ from $- 4 x$ .

$- 12 x \leq - 6$

Step 5

Divide each term in $- 12 x \leq - 6$ by $- 12$ and simplify.

Divide each term in $- 12 x \leq - 6$ by $- 12$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 12 x}{- 12} \geq \frac{- 6}{- 12}$

Simplify the left side.

Cancel the common factor of $- 12$ .

Cancel the common factor.

$\frac{- 12 x}{- 12} \geq \frac{- 6}{- 12}$

Divide $x$ by $1$ .

$x \geq \frac{- 6}{- 12}$

Simplify the right side.

Cancel the common factor of $- 6$ and $- 12$ .

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

$x \geq \frac{- 6 (1)}{- 12}$

Cancel the common factors.

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

$x \geq \frac{- 6 \cdot 1}{- 6 \cdot 2}$

Cancel the common factor.

$x \geq \frac{- 6 \cdot 1}{- 6 \cdot 2}$

Rewrite the expression.

$x \geq \frac{1}{2}$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x \geq \frac{1}{2}$

Interval Notation:

$[\frac{1}{2}, \infty)$

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

Related Questions

Support LCMGCF.com by disabling your adblocker.