Solve the Inequality for x 2(6x-10)<=31-3(5-3x)

$2 (6 x - 10) \leq 31 - 3 (5 - 3 x)$

Step 1

Simplify $2 (6 x - 10)$ .

Rewrite.

$0 + 0 + 2 (6 x - 10) \leq 31 - 3 (5 - 3 x)$

Simplify by adding zeros.

$2 (6 x - 10) \leq 31 - 3 (5 - 3 x)$

Apply the distributive property.

$2 (6 x) + 2 \cdot - 10 \leq 31 - 3 (5 - 3 x)$

Multiply.

Multiply $6$ by $2$ .

$12 x + 2 \cdot - 10 \leq 31 - 3 (5 - 3 x)$

Multiply $2$ by $- 10$ .

$12 x - 20 \leq 31 - 3 (5 - 3 x)$

Step 2

Simplify $31 - 3 (5 - 3 x)$ .

Simplify each term.

Apply the distributive property.

$12 x - 20 \leq 31 - 3 \cdot 5 - 3 (- 3 x)$

Multiply $- 3$ by $5$ .

$12 x - 20 \leq 31 - 15 - 3 (- 3 x)$

Multiply $- 3$ by $- 3$ .

$12 x - 20 \leq 31 - 15 + 9 x$

Subtract $15$ from $31$ .

$12 x - 20 \leq 16 + 9 x$

Step 3

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

Subtract $9 x$ from both sides of the inequality.

$12 x - 20 - 9 x \leq 16$

Subtract $9 x$ from $12 x$ .

$3 x - 20 \leq 16$

Step 4

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

Add $20$ to both sides of the inequality.

$3 x \leq 16 + 20$

Add $16$ and $20$ .

$3 x \leq 36$

Step 5

Divide each term in $3 x \leq 36$ by $3$ and simplify.

Divide each term in $3 x \leq 36$ by $3$ .

$\frac{3 x}{3} \leq \frac{36}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} \leq \frac{36}{3}$

Divide $x$ by $1$ .

$x \leq \frac{36}{3}$

Simplify the right side.

Divide $36$ by $3$ .

$x \leq 12$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x \leq 12$

Interval Notation:

$(- \infty, 12]$

Solve the Inequality for x 2(6x-10)<=31-3(5-3x)

Related Questions

Support LCMGCF.com by disabling your adblocker.