Solve for x 9-2x<7+2(x-3)

$9 - 2 x < 7 + 2 (x - 3)$

Step 1

Simplify $7 + 2 (x - 3)$ .

Simplify each term.

Apply the distributive property.

$9 - 2 x < 7 + 2 x + 2 \cdot - 3$

Multiply $2$ by $- 3$ .

$9 - 2 x < 7 + 2 x - 6$

Subtract $6$ from $7$ .

$9 - 2 x < 2 x + 1$

Step 2

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

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

$9 - 2 x - 2 x < 1$

Subtract $2 x$ from $- 2 x$ .

$9 - 4 x < 1$

Step 3

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

Subtract $9$ from both sides of the inequality.

$- 4 x < 1 - 9$

Subtract $9$ from $1$ .

$- 4 x < - 8$

Step 4

Divide each term in $- 4 x < - 8$ by $- 4$ and simplify.

Divide each term in $- 4 x < - 8$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 4 x}{- 4} > \frac{- 8}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} > \frac{- 8}{- 4}$

Divide $x$ by $1$ .

$x > \frac{- 8}{- 4}$

Simplify the right side.

Divide $- 8$ by $- 4$ .

$x > 2$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x > 2$

Interval Notation:

$(2, \infty)$

Solve for x 9-2x<7+2(x-3)

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