Solve for x 2x-6>=6(x-2)+8

$2 x - 6 \geq 6 (x - 2) + 8$

Step 1

Simplify $6 (x - 2) + 8$ .

Simplify each term.

Apply the distributive property.

$2 x - 6 \geq 6 x + 6 \cdot - 2 + 8$

Multiply $6$ by $- 2$ .

$2 x - 6 \geq 6 x - 12 + 8$

Add $- 12$ and $8$ .

$2 x - 6 \geq 6 x - 4$

Step 2

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

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

$2 x - 6 - 6 x \geq - 4$

Subtract $6 x$ from $2 x$ .

$- 4 x - 6 \geq - 4$

Step 3

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

Add $6$ to both sides of the inequality.

$- 4 x \geq - 4 + 6$

Add $- 4$ and $6$ .

$- 4 x \geq 2$

Step 4

Divide each term in $- 4 x \geq 2$ by $- 4$ and simplify.

Divide each term in $- 4 x \geq 2$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 4 x}{- 4} \leq \frac{2}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} \leq \frac{2}{- 4}$

Divide $x$ by $1$ .

$x \leq \frac{2}{- 4}$

Simplify the right side.

Cancel the common factor of $2$ and $- 4$ .

Factor $2$ out of $2$ .

$x \leq \frac{2 (1)}{- 4}$

Cancel the common factors.

Factor $2$ out of $- 4$ .

$x \leq \frac{2 \cdot 1}{2 \cdot - 2}$

Cancel the common factor.

$x \leq \frac{2 \cdot 1}{2 \cdot - 2}$

Rewrite the expression.

$x \leq \frac{1}{- 2}$

Move the negative in front of the fraction.

$x \leq - \frac{1}{2}$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x \leq - \frac{1}{2}$

Interval Notation:

$(- \infty, - \frac{1}{2}]$

Solve for x 2x-6>=6(x-2)+8

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