Solve the Inequality for x 5(x-1)-2(x-3)>=13

$5 (x - 1) - 2 (x - 3) \geq 13$

Step 1

Simplify $5 (x - 1) - 2 (x - 3)$ .

Simplify each term.

Apply the distributive property.

$5 x + 5 \cdot - 1 - 2 (x - 3) \geq 13$

Multiply $5$ by $- 1$ .

$5 x - 5 - 2 (x - 3) \geq 13$

Apply the distributive property.

$5 x - 5 - 2 x - 2 \cdot - 3 \geq 13$

Multiply $- 2$ by $- 3$ .

$5 x - 5 - 2 x + 6 \geq 13$

Simplify by adding terms.

Subtract $2 x$ from $5 x$ .

$3 x - 5 + 6 \geq 13$

Add $- 5$ and $6$ .

$3 x + 1 \geq 13$

Step 2

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

Subtract $1$ from both sides of the inequality.

$3 x \geq 13 - 1$

Subtract $1$ from $13$ .

$3 x \geq 12$

Step 3

Divide each term in $3 x \geq 12$ by $3$ and simplify.

Divide each term in $3 x \geq 12$ by $3$ .

$\frac{3 x}{3} \geq \frac{12}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} \geq \frac{12}{3}$

Divide $x$ by $1$ .

$x \geq \frac{12}{3}$

Simplify the right side.

Divide $12$ by $3$ .

$x \geq 4$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \geq 4$

Interval Notation:

$[4, \infty)$