Question

Solve for x: 4x+1/2(2x+4) >12

Answer 1

Answer: x>2

Explanation:

`4x+(1)/(2) (2x+4) > 12`

Step 1: Simplify both sides of the inequality through the Distributive Property

`4x+(1)/(2) (2x+4) > 12\\4x+((1)/(2))(2x)+((1)/(2))(4) > 12\\4x+x+2 > 12\\5x+2 > 12`

Step 2: Subtract 2 from both sides to isolate x

`5x+2-2 > 12-2\\5x > 10`

Step 3: Divide both sides by 5 to full isolate x

`(5x)/(5) > (10)/(5) \\x > 2`

Answer 2

`x > 2`

Explanation:

`4x+(1)/(2)(2x+4) > 12 < ==multiply\ the\ \#s\ in\ the\ parenthesis\ first\ using\ (1)/(2)\\\\4x+x+2 > 12 < ==combine\ any\ like\ terms\\\\5x+2 > 12 < ==subtract\ 2\ from\ both\ sides\\-2 \ \ \ \ \ -2\\\\5x > 10 < ==divide\ both\ sides\ by\ 5\\/5 \ \ \ \ /5\\\\x > 2`

This means that x can be any value that is greater than 2.

Hope this helps!