Solve the Inequality for x 7x+5<2x-10

$7 x + 5 < 2 x - 10$

Step 1

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

Subtract $2 x$ from both sides of the inequality.

$7 x + 5 - 2 x < - 10$

Subtract $2 x$ from $7 x$ .

$5 x + 5 < - 10$

Step 2

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

Subtract $5$ from both sides of the inequality.

$5 x < - 10 - 5$

Subtract $5$ from $- 10$ .

$5 x < - 15$

Step 3

Divide each term in $5 x < - 15$ by $5$ and simplify.

Divide each term in $5 x < - 15$ by $5$ .

$\frac{5 x}{5} < \frac{- 15}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} < \frac{- 15}{5}$

Divide $x$ by $1$ .

$x < \frac{- 15}{5}$

Simplify the right side.

Divide $- 15$ by $5$ .

$x < - 3$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x < - 3$

Interval Notation:

$(- \infty, - 3)$