Solve the Inequality for x 6x-20>3(2-x)+6x-2

$6 x - 20 > 3 (2 - x) + 6 x - 2$

Step 1

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

$3 (2 - x) + 6 x - 2 < 6 x - 20$

Step 2

Simplify $3 (2 - x) + 6 x - 2$ .

Simplify each term.

Apply the distributive property.

$3 \cdot 2 + 3 (- x) + 6 x - 2 < 6 x - 20$

Multiply $3$ by $2$ .

$6 + 3 (- x) + 6 x - 2 < 6 x - 20$

Multiply $- 1$ by $3$ .

$6 - 3 x + 6 x - 2 < 6 x - 20$

Simplify by adding terms.

Subtract $2$ from $6$ .

$- 3 x + 6 x + 4 < 6 x - 20$

Add $- 3 x$ and $6 x$ .

$3 x + 4 < 6 x - 20$

Step 3

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

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

$3 x + 4 - 6 x < - 20$

Subtract $6 x$ from $3 x$ .

$- 3 x + 4 < - 20$

Step 4

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

Subtract $4$ from both sides of the inequality.

$- 3 x < - 20 - 4$

Subtract $4$ from $- 20$ .

$- 3 x < - 24$

Step 5

Divide each term in $- 3 x < - 24$ by $- 3$ and simplify.

Divide each term in $- 3 x < - 24$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 x}{- 3} > \frac{- 24}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} > \frac{- 24}{- 3}$

Divide $x$ by $1$ .

$x > \frac{- 24}{- 3}$

Simplify the right side.

Divide $- 24$ by $- 3$ .

$x > 8$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x > 8$

Interval Notation:

$(8, \infty)$

Solve the Inequality for x 6x-20>3(2-x)+6x-2

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