Solve the Inequality for x -6+8(6x+2)<7x+10

$- 6 + 8 (6 x + 2) < 7 x + 10$

Simplify $- 6 + 8 (6 x + 2)$ .

Simplify each term.

Apply the distributive property.

$- 6 + 8 (6 x) + 8 \cdot 2 < 7 x + 10$

Multiply $6$ by $8$ .

$- 6 + 48 x + 8 \cdot 2 < 7 x + 10$

Multiply $8$ by $2$ .

$- 6 + 48 x + 16 < 7 x + 10$

Add $- 6$ and $16$ .

$48 x + 10 < 7 x + 10$

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

Subtract $7 x$ from both sides of the inequality.

$48 x + 10 - 7 x < 10$

Subtract $7 x$ from $48 x$ .

$41 x + 10 < 10$

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

Subtract $10$ from both sides of the inequality.

$41 x < 10 - 10$

Subtract $10$ from $10$ .

$41 x < 0$

Divide each term in $41 x < 0$ by $41$ and simplify.

Divide each term in $41 x < 0$ by $41$ .

$\frac{41 x}{41} < \frac{0}{41}$

Simplify the left side.

Cancel the common factor of $41$ .

Cancel the common factor.

$\frac{41 x}{41} < \frac{0}{41}$

Divide $x$ by $1$ .

$x < \frac{0}{41}$

Simplify the right side.

Divide $0$ by $41$ .

$x < 0$

The result can be shown in multiple forms.

Inequality Form:

$x < 0$

Interval Notation:

$(- \infty, 0)$