Question

Can I get some help with this question? Solve 3(x + 2) > x.

Answer 1

x > -3

Explanation:

We are given the following inequality that we are to solve:

`3(x+2)>x`

Applying the distributive property of multiplication on the left side of the inequality to get:

`3 x + 6 > x`

Rearranging the inequality:

`3 x - x > - 6`

`2 x > - 6`

`x > \frac { - 6 } { 2 }`

x > -3

Answer 2

`\large\boxed{x>-3\to\\ x>-3\\to x\in(-3,\ \infty)}`

Explanation:

`3(x+2)>x\qquad\text{use the distributive property:}\ a(b+c)=ab+ac\\\\(3)(x)+(3)(2)>x\\\\3x+6>x\qquad\text{subtract 6 from both sides}\\\\3x+6-6>x-6\\\\3x>x-6\qquad\text{subtract x from both sides}\\\\3x-x>x-x-6\\\\2x>-6\qquad\text{divide both sides by 2}\\\\(2x)/(2)>(-6)/(2)\\\\x>-3`