Solve the Inequality for x 1/2(-2x-10)>3(4-6x)

$\frac{1}{2} (- 2 x - 10) > 3 (4 - 6 x)$

Simplify $\frac{1}{2} \cdot (- 2 x - 10)$ .

Start simplifying.

$0 + 0 + \frac{1}{2} \cdot (- 2 x - 10) > 3 (4 - 6 x)$

Simplify by adding zeros.

$\frac{1}{2} \cdot (- 2 x - 10) > 3 (4 - 6 x)$

Apply the distributive property.

$\frac{1}{2} (- 2 x) + \frac{1}{2} \cdot - 10 > 3 (4 - 6 x)$

Cancel the common factor of $2$ .

Factor $2$ out of $- 2 x$ .

$\frac{1}{2} (2 (- x)) + \frac{1}{2} \cdot - 10 > 3 (4 - 6 x)$

Cancel the common factor.

$\frac{1}{2} (2 (- x)) + \frac{1}{2} \cdot - 10 > 3 (4 - 6 x)$

Rewrite the expression.

$- x + \frac{1}{2} \cdot - 10 > 3 (4 - 6 x)$

Cancel the common factor of $2$ .

Factor $2$ out of $- 10$ .

$- x + \frac{1}{2} \cdot (2 (- 5)) > 3 (4 - 6 x)$

Cancel the common factor.

$- x + \frac{1}{2} \cdot (2 \cdot - 5) > 3 (4 - 6 x)$

Rewrite the expression.

$- x - 5 > 3 (4 - 6 x)$

Simplify $3 (4 - 6 x)$ .

Apply the distributive property.

$- x - 5 > 3 \cdot 4 + 3 (- 6 x)$

Multiply.

Multiply $3$ by $4$ .

$- x - 5 > 12 + 3 (- 6 x)$

Multiply $- 6$ by $3$ .

$- x - 5 > 12 - 18 x$

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

Add $18 x$ to both sides of the inequality.

$- x - 5 + 18 x > 12$

Add $- x$ and $18 x$ .

$17 x - 5 > 12$

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

Add $5$ to both sides of the inequality.

$17 x > 12 + 5$

Add $12$ and $5$ .

$17 x > 17$

Divide each term in $17 x > 17$ by $17$ and simplify.

Divide each term in $17 x > 17$ by $17$ .

$\frac{17 x}{17} > \frac{17}{17}$

Simplify the left side.

Cancel the common factor of $17$ .

Cancel the common factor.

$\frac{17 x}{17} > \frac{17}{17}$

Divide $x$ by $1$ .

$x > \frac{17}{17}$

Simplify the right side.

Divide $17$ by $17$ .

$x > 1$

The result can be shown in multiple forms.

Inequality Form:

$x > 1$

Interval Notation:

$(1, \infty)$

Solve the Inequality for x 1/2(-2x-10)>3(4-6x)

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