Inequality plz help! easy!?

Question

Define a variable, write an inequality, and solve each problem. Check your solution. I am wondering how to check the solution btw..

1) The sum of three times a number and -4 is at least twice the number plus 8

THANKS :)

Answer 1

Let x be a number,

The word 'at least ' represents more than or equal and symbol is ≥.

So, 3x - 4 ≥ 2x + 8

Add 4 to each side.

3x ≥ 2x + 12

Subtract 2x from each side.

x ≥ 12

Check: 3x - 4 ≥ 2x + 8

substitute x = 12 in the equation.

3(12) - 4 ≥ 2(12) + 8

36 - 4 ≥ 24 + 8

32 ≥ 32

The equation is true.

The solutions set is {x | x ≥ 12 }