Solve the Inequality for x -3(7x+3)<6x

$- 3 (7 x + 3) < 6 x$

Step 1

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

Rewrite.

$0 + 0 - 3 (7 x + 3) < 6 x$

Simplify by adding zeros.

$- 3 (7 x + 3) < 6 x$

Apply the distributive property.

$- 3 (7 x) - 3 \cdot 3 < 6 x$

Multiply.

Multiply $7$ by $- 3$ .

$- 21 x - 3 \cdot 3 < 6 x$

Multiply $- 3$ by $3$ .

$- 21 x - 9 < 6 x$

Step 2

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

Subtract $6 x$ from both sides of the inequality.

$- 21 x - 9 - 6 x < 0$

Subtract $6 x$ from $- 21 x$ .

$- 27 x - 9 < 0$

Step 3

Add $9$ to both sides of the inequality.

$- 27 x < 9$

Step 4

Divide each term in $- 27 x < 9$ by $- 27$ and simplify.

Divide each term in $- 27 x < 9$ by $- 27$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 27 x}{- 27} > \frac{9}{- 27}$

Simplify the left side.

Cancel the common factor of $- 27$ .

Cancel the common factor.

$\frac{- 27 x}{- 27} > \frac{9}{- 27}$

Divide $x$ by $1$ .

$x > \frac{9}{- 27}$

Simplify the right side.

Cancel the common factor of $9$ and $- 27$ .

Factor $9$ out of $9$ .

$x > \frac{9 (1)}{- 27}$

Cancel the common factors.

Factor $9$ out of $- 27$ .

$x > \frac{9 \cdot 1}{9 \cdot - 3}$

Cancel the common factor.

$x > \frac{9 \cdot 1}{9 \cdot - 3}$

Rewrite the expression.

$x > \frac{1}{- 3}$

Move the negative in front of the fraction.

$x > - \frac{1}{3}$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x > - \frac{1}{3}$

Interval Notation:

$(- \frac{1}{3}, \infty)$

Solve the Inequality for x -3(7x+3)<6x

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