Solve the Inequality for x 7x-2<=9x+3

$7 x - 2 \leq 9 x + 3$

Step 1

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

Subtract $9 x$ from both sides of the inequality.

$7 x - 2 - 9 x \leq 3$

Subtract $9 x$ from $7 x$ .

$- 2 x - 2 \leq 3$

Step 2

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

Add $2$ to both sides of the inequality.

$- 2 x \leq 3 + 2$

Add $3$ and $2$ .

$- 2 x \leq 5$

Step 3

Divide each term in $- 2 x \leq 5$ by $- 2$ and simplify.

Divide each term in $- 2 x \leq 5$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 x}{- 2} \geq \frac{5}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} \geq \frac{5}{- 2}$

Divide $x$ by $1$ .

$x \geq \frac{5}{- 2}$

Simplify the right side.

Move the negative in front of the fraction.

$x \geq - \frac{5}{2}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \geq - \frac{5}{2}$

Interval Notation:

$[- \frac{5}{2}, \infty)$

Solve the Inequality for x 7x-2<=9x+3

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