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

$x - 7 < 2 x - 5$

Step 1

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

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

$x - 7 - 2 x < - 5$

Subtract $2 x$ from $x$ .

$- x - 7 < - 5$

Step 2

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

Add $7$ to both sides of the inequality.

$- x < - 5 + 7$

Add $- 5$ and $7$ .

$- x < 2$

Step 3

Divide each term in $- x < 2$ by $- 1$ and simplify.

Divide each term in $- x < 2$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} > \frac{2}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} > \frac{2}{- 1}$

Divide $x$ by $1$ .

$x > \frac{2}{- 1}$

Simplify the right side.

Divide $2$ by $- 1$ .

$x > - 2$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x > - 2$

Interval Notation:

$(- 2, \infty)$

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

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