Solve the Inequality for x 4x+7(3x-3)<=9-5x

$4 x + 7 (3 x - 3) \leq 9 - 5 x$

Step 1

Simplify $4 x + 7 (3 x - 3)$ .

Simplify each term.

Apply the distributive property.

$4 x + 7 (3 x) + 7 \cdot - 3 \leq 9 - 5 x$

Multiply $3$ by $7$ .

$4 x + 21 x + 7 \cdot - 3 \leq 9 - 5 x$

Multiply $7$ by $- 3$ .

$4 x + 21 x - 21 \leq 9 - 5 x$

Add $4 x$ and $21 x$ .

$25 x - 21 \leq 9 - 5 x$

Step 2

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

Add $5 x$ to both sides of the inequality.

$25 x - 21 + 5 x \leq 9$

Add $25 x$ and $5 x$ .

$30 x - 21 \leq 9$

Step 3

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

Add $21$ to both sides of the inequality.

$30 x \leq 9 + 21$

Add $9$ and $21$ .

$30 x \leq 30$

Step 4

Divide each term in $30 x \leq 30$ by $30$ and simplify.

Divide each term in $30 x \leq 30$ by $30$ .

$\frac{30 x}{30} \leq \frac{30}{30}$

Simplify the left side.

Cancel the common factor of $30$ .

Cancel the common factor.

$\frac{30 x}{30} \leq \frac{30}{30}$

Divide $x$ by $1$ .

$x \leq \frac{30}{30}$

Simplify the right side.

Divide $30$ by $30$ .

$x \leq 1$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x \leq 1$

Interval Notation:

$(- \infty, 1]$