Solve the Inequality for x 5x-6<=2+(3x-4)

$5 x - 6 \leq 2 + (3 x - 4)$

Step 1

Subtract $4$ from $2$ .

$5 x - 6 \leq 3 x - 2$

Step 2

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

Subtract $3 x$ from both sides of the inequality.

$5 x - 6 - 3 x \leq - 2$

Subtract $3 x$ from $5 x$ .

$2 x - 6 \leq - 2$

Step 3

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

Add $6$ to both sides of the inequality.

$2 x \leq - 2 + 6$

Add $- 2$ and $6$ .

$2 x \leq 4$

Step 4

Divide each term in $2 x \leq 4$ by $2$ and simplify.

Divide each term in $2 x \leq 4$ by $2$ .

$\frac{2 x}{2} \leq \frac{4}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} \leq \frac{4}{2}$

Divide $x$ by $1$ .

$x \leq \frac{4}{2}$

Simplify the right side.

Divide $4$ by $2$ .

$x \leq 2$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x \leq 2$

Interval Notation:

$(- \infty, 2]$