Solve for x 8x>4(x+4)-6

$8 x > 4 (x + 4) - 6$

Step 1

Simplify $4 (x + 4) - 6$ .

Simplify each term.

Apply the distributive property.

$8 x > 4 x + 4 \cdot 4 - 6$

Multiply $4$ by $4$ .

$8 x > 4 x + 16 - 6$

Subtract $6$ from $16$ .

$8 x > 4 x + 10$

Step 2

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

Subtract $4 x$ from both sides of the inequality.

$8 x - 4 x > 10$

Subtract $4 x$ from $8 x$ .

$4 x > 10$

Step 3

Divide each term in $4 x > 10$ by $4$ and simplify.

Divide each term in $4 x > 10$ by $4$ .

$\frac{4 x}{4} > \frac{10}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} > \frac{10}{4}$

Divide $x$ by $1$ .

$x > \frac{10}{4}$

Simplify the right side.

Cancel the common factor of $10$ and $4$ .

Factor $2$ out of $10$ .

$x > \frac{2 (5)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$x > \frac{2 \cdot 5}{2 \cdot 2}$

Cancel the common factor.

$x > \frac{2 \cdot 5}{2 \cdot 2}$

Rewrite the expression.

$x > \frac{5}{2}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x > \frac{5}{2}$

Interval Notation:

$(\frac{5}{2}, \infty)$