Solve for x 4(x-3)-2(x-1)>0

$4 (x - 3) - 2 (x - 1) > 0$

Step 1

Simplify $4 (x - 3) - 2 (x - 1)$ .

Simplify each term.

Apply the distributive property.

$4 x + 4 \cdot - 3 - 2 (x - 1) > 0$

Multiply $4$ by $- 3$ .

$4 x - 12 - 2 (x - 1) > 0$

Apply the distributive property.

$4 x - 12 - 2 x - 2 \cdot - 1 > 0$

Multiply $- 2$ by $- 1$ .

$4 x - 12 - 2 x + 2 > 0$

$4 x - 12 - 2 x + 2 > 0$

Simplify by adding terms.

Subtract $2 x$ from $4 x$ .

$2 x - 12 + 2 > 0$

Add $- 12$ and $2$ .

$2 x - 10 > 0$

$2 x - 10 > 0$

$2 x - 10 > 0$

Step 2

Add $10$ to both sides of the inequality.

$2 x > 10$

Step 3

Divide each term in $2 x > 10$ by $2$ and simplify.

Divide each term in $2 x > 10$ by $2$ .

$\frac{2 x}{2} > \frac{10}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} > \frac{10}{2}$

Divide $x$ by $1$ .

$x > \frac{10}{2}$

$x > \frac{10}{2}$

$x > \frac{10}{2}$

Simplify the right side.

Divide $10$ by $2$ .

$x > 5$

$x > 5$

$x > 5$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x > 5$

Interval Notation:

$(5, \infty)$

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