Solve the Inequality for x 3(x-5)<2(2x-1)

$3 (x - 5) < 2 (2 x - 1)$

Step 1

Simplify $3 (x - 5)$ .

Start simplifying.

$0 + 0 + 3 (x - 5) < 2 (2 x - 1)$

Simplify by adding zeros.

$3 (x - 5) < 2 (2 x - 1)$

Apply the distributive property.

$3 x + 3 \cdot - 5 < 2 (2 x - 1)$

Multiply $3$ by $- 5$ .

$3 x - 15 < 2 (2 x - 1)$

Step 2

Simplify $2 (2 x - 1)$ .

Apply the distributive property.

$3 x - 15 < 2 (2 x) + 2 \cdot - 1$

Multiply.

Multiply $2$ by $2$ .

$3 x - 15 < 4 x + 2 \cdot - 1$

Multiply $2$ by $- 1$ .

$3 x - 15 < 4 x - 2$

Step 3

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

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

$3 x - 15 - 4 x < - 2$

Subtract $4 x$ from $3 x$ .

$- x - 15 < - 2$

Step 4

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

Add $15$ to both sides of the inequality.

$- x < - 2 + 15$

Add $- 2$ and $15$ .

$- x < 13$

Step 5

Divide each term in $- x < 13$ by $- 1$ and simplify.

Divide each term in $- x < 13$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} > \frac{13}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} > \frac{13}{- 1}$

Divide $x$ by $1$ .

$x > \frac{13}{- 1}$

Simplify the right side.

Divide $13$ by $- 1$ .

$x > - 13$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x > - 13$

Interval Notation:

$(- 13, \infty)$

Solve the Inequality for x 3(x-5)<2(2x-1)

Related Questions

Support LCMGCF.com by disabling your adblocker.