Solve the Inequality for x 2x-(6x+7)>-19

$2 x - (6 x + 7) > - 19$

Step 1

Simplify $2 x - (6 x + 7)$ .

Simplify each term.

Apply the distributive property.

$2 x - (6 x) - 1 \cdot 7 > - 19$

Multiply $6$ by $- 1$ .

$2 x - 6 x - 1 \cdot 7 > - 19$

Multiply $- 1$ by $7$ .

$2 x - 6 x - 7 > - 19$

Subtract $6 x$ from $2 x$ .

$- 4 x - 7 > - 19$

Step 2

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

Add $7$ to both sides of the inequality.

$- 4 x > - 19 + 7$

Add $- 19$ and $7$ .

$- 4 x > - 12$

Step 3

Divide each term in $- 4 x > - 12$ by $- 4$ and simplify.

Divide each term in $- 4 x > - 12$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 4 x}{- 4} < \frac{- 12}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} < \frac{- 12}{- 4}$

Divide $x$ by $1$ .

$x < \frac{- 12}{- 4}$

Simplify the right side.

Divide $- 12$ by $- 4$ .

$x < 3$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x < 3$

Interval Notation:

$(- \infty, 3)$

Solve the Inequality for x 2x-(6x+7)>-19

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