Solve the Inequality for x 2(7x-3)<=12x+16

$2 (7 x - 3) \leq 12 x + 16$

Simplify $2 (7 x - 3)$ .

Rewrite.

$0 + 0 + 2 (7 x - 3) \leq 12 x + 16$

Simplify by adding zeros.

$2 (7 x - 3) \leq 12 x + 16$

Apply the distributive property.

$2 (7 x) + 2 \cdot - 3 \leq 12 x + 16$

Multiply.

Multiply $7$ by $2$ .

$14 x + 2 \cdot - 3 \leq 12 x + 16$

Multiply $2$ by $- 3$ .

$14 x - 6 \leq 12 x + 16$

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

Subtract $12 x$ from both sides of the inequality.

$14 x - 6 - 12 x \leq 16$

Subtract $12 x$ from $14 x$ .

$2 x - 6 \leq 16$

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

Add $6$ to both sides of the inequality.

$2 x \leq 16 + 6$

Add $16$ and $6$ .

$2 x \leq 22$

Divide each term in $2 x \leq 22$ by $2$ and simplify.

Divide each term in $2 x \leq 22$ by $2$ .

$\frac{2 x}{2} \leq \frac{22}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} \leq \frac{22}{2}$

Divide $x$ by $1$ .

$x \leq \frac{22}{2}$

Simplify the right side.

Divide $22$ by $2$ .

$x \leq 11$

The result can be shown in multiple forms.

Inequality Form:

$x \leq 11$

Interval Notation:

$(- \infty, 11]$