Solve for x 3(2x-1)-11x<=-3x+5

$3 (2 x - 1) - 11 x \leq - 3 x + 5$

Step 1

Simplify $3 (2 x - 1) - 11 x$ .

Simplify each term.

Apply the distributive property.

$3 (2 x) + 3 \cdot - 1 - 11 x \leq - 3 x + 5$

Multiply $2$ by $3$ .

$6 x + 3 \cdot - 1 - 11 x \leq - 3 x + 5$

Multiply $3$ by $- 1$ .

$6 x - 3 - 11 x \leq - 3 x + 5$

Subtract $11 x$ from $6 x$ .

$- 5 x - 3 \leq - 3 x + 5$

Step 2

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

Add $3 x$ to both sides of the inequality.

$- 5 x - 3 + 3 x \leq 5$

Add $- 5 x$ and $3 x$ .

$- 2 x - 3 \leq 5$

Step 3

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

Add $3$ to both sides of the inequality.

$- 2 x \leq 5 + 3$

Add $5$ and $3$ .

$- 2 x \leq 8$

Step 4

Divide each term in $- 2 x \leq 8$ by $- 2$ and simplify.

Divide each term in $- 2 x \leq 8$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 x}{- 2} \geq \frac{8}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} \geq \frac{8}{- 2}$

Divide $x$ by $1$ .

$x \geq \frac{8}{- 2}$

Simplify the right side.

Divide $8$ by $- 2$ .

$x \geq - 4$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x \geq - 4$

Interval Notation:

$[- 4, \infty)$

Solve for x 3(2x-1)-11x<=-3x+5

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