Solve the Inequality for x 3x-4>4-(x+6)

$3 x - 4 > 4 - (x + 6)$

Step 1

Simplify $4 - (x + 6)$ .

Simplify each term.

Apply the distributive property.

$3 x - 4 > 4 - x - 1 \cdot 6$

Multiply $- 1$ by $6$ .

$3 x - 4 > 4 - x - 6$

Subtract $6$ from $4$ .

$3 x - 4 > - x - 2$

Step 2

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

Add $x$ to both sides of the inequality.

$3 x - 4 + x > - 2$

Add $3 x$ and $x$ .

$4 x - 4 > - 2$

Step 3

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

Add $4$ to both sides of the inequality.

$4 x > - 2 + 4$

Add $- 2$ and $4$ .

$4 x > 2$

Step 4

Divide each term in $4 x > 2$ by $4$ and simplify.

Divide each term in $4 x > 2$ by $4$ .

$\frac{4 x}{4} > \frac{2}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} > \frac{2}{4}$

Divide $x$ by $1$ .

$x > \frac{2}{4}$

Simplify the right side.

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $2$ .

$x > \frac{2 (1)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$x > \frac{2 \cdot 1}{2 \cdot 2}$

Cancel the common factor.

$x > \frac{2 \cdot 1}{2 \cdot 2}$

Rewrite the expression.

$x > \frac{1}{2}$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x > \frac{1}{2}$

Interval Notation:

$(\frac{1}{2}, \infty)$

Solve the Inequality for x 3x-4>4-(x+6)

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