Solve the Inequality for x -9(x-5)+9<3x+42

$- 9 (x - 5) + 9 < 3 x + 42$

Step 1

Simplify $- 9 (x - 5) + 9$ .

Simplify each term.

Apply the distributive property.

$- 9 x - 9 \cdot - 5 + 9 < 3 x + 42$

Multiply $- 9$ by $- 5$ .

$- 9 x + 45 + 9 < 3 x + 42$

Add $45$ and $9$ .

$- 9 x + 54 < 3 x + 42$

Step 2

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

Subtract $3 x$ from both sides of the inequality.

$- 9 x + 54 - 3 x < 42$

Subtract $3 x$ from $- 9 x$ .

$- 12 x + 54 < 42$

Step 3

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

Subtract $54$ from both sides of the inequality.

$- 12 x < 42 - 54$

Subtract $54$ from $42$ .

$- 12 x < - 12$

Step 4

Divide each term in $- 12 x < - 12$ by $- 12$ and simplify.

Divide each term in $- 12 x < - 12$ by $- 12$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 12 x}{- 12} > \frac{- 12}{- 12}$

Simplify the left side.

Cancel the common factor of $- 12$ .

Cancel the common factor.

$\frac{- 12 x}{- 12} > \frac{- 12}{- 12}$

Divide $x$ by $1$ .

$x > \frac{- 12}{- 12}$

Simplify the right side.

Divide $- 12$ by $- 12$ .

$x > 1$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x > 1$

Interval Notation:

$(1, \infty)$

Solve the Inequality for x -9(x-5)+9<3x+42

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