Solve the Inequality for x 6(3x-7)<=7x+13

$6 (3 x - 7) \leq 7 x + 13$

Simplify $6 (3 x - 7)$ .

Rewrite.

$0 + 0 + 6 (3 x - 7) \leq 7 x + 13$

Simplify by adding zeros.

$6 (3 x - 7) \leq 7 x + 13$

Apply the distributive property.

$6 (3 x) + 6 \cdot - 7 \leq 7 x + 13$

Multiply.

Multiply $3$ by $6$ .

$18 x + 6 \cdot - 7 \leq 7 x + 13$

Multiply $6$ by $- 7$ .

$18 x - 42 \leq 7 x + 13$

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

Subtract $7 x$ from both sides of the inequality.

$18 x - 42 - 7 x \leq 13$

Subtract $7 x$ from $18 x$ .

$11 x - 42 \leq 13$

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

Add $42$ to both sides of the inequality.

$11 x \leq 13 + 42$

Add $13$ and $42$ .

$11 x \leq 55$

Divide each term in $11 x \leq 55$ by $11$ and simplify.

Divide each term in $11 x \leq 55$ by $11$ .

$\frac{11 x}{11} \leq \frac{55}{11}$

Simplify the left side.

Cancel the common factor of $11$ .

Cancel the common factor.

$\frac{11 x}{11} \leq \frac{55}{11}$

Divide $x$ by $1$ .

$x \leq \frac{55}{11}$

Simplify the right side.

Divide $55$ by $11$ .

$x \leq 5$

The result can be shown in multiple forms.

Inequality Form:

$x \leq 5$

Interval Notation:

$(- \infty, 5]$