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

$4 (5 + 2^{2}) < 3 (3 - x)$

Step 1

Rewrite so $x$ is on the left side of the inequality.

$3 (3 - x) > 4 (5 + 2^{2})$

Step 2

Simplify.

Raise $2$ to the power of $2$ .

$3 (3 - x) > 4 (5 + 4)$

Add $5$ and $4$ .

$3 (3 - x) > 4 \cdot 9$

Multiply $4$ by $9$ .

$3 (3 - x) > 36$

Step 3

Divide each term in $3 (3 - x) > 36$ by $3$ and simplify.

Divide each term in $3 (3 - x) > 36$ by $3$ .

$\frac{3 (3 - x)}{3} > \frac{36}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 (3 - x)}{3} > \frac{36}{3}$

Divide $3 - x$ by $1$ .

$3 - x > \frac{36}{3}$

Simplify the right side.

Divide $36$ by $3$ .

$3 - x > 12$

Step 4

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

Subtract $3$ from both sides of the inequality.

$- x > 12 - 3$

Subtract $3$ from $12$ .

$- x > 9$

Step 5

Divide each term in $- x > 9$ by $- 1$ and simplify.

Divide each term in $- x > 9$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} < \frac{9}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} < \frac{9}{- 1}$

Divide $x$ by $1$ .

$x < \frac{9}{- 1}$

Simplify the right side.

Divide $9$ by $- 1$ .

$x < - 9$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x < - 9$

Interval Notation:

$(- \infty, - 9)$

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

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