Question 132450
6(x+3)-2(x+5) ≥ 7(x+1)-2

Why not treat this like a regular linear equation?

In other words, disregard the ≥ and treat this question like you would a linear equation having, of course, an equal sign.

The first thing you want to do is remove the parentheses by using the distributive rule.

6(x + 3) becomes 6x + 18
-2(x + 5) becomes -2x - 10
7(x + 1) becomes 7x + 7

We now have this set up:

6x + 18 - 2x - 10 ≥ 7x + 7 - 2

Next, combine like terms on both sides of the inequality.

4x + 8 ≥ 7x + 5

Combine like terms again and simplify to finish.

4x - 7x ≥ -8 + 5

-3x ≥ -3

Divide both sides of the inequality by -3 to find x.  In the world of inequalities, when you divide both sides by a negative number, you MUST reverse the sign of the inequality in your answer.  Is this clear?  In other words, ≥ will become ≤, which means less than or equal to.  

x ≤ -3/-3

x ≤ 1....Done!

What does the answer above mean?  The answer x ≤ 1 means that the value of x must be less than or equal to 1 in order to make the original inequality a TRUE statement.  If you replace x with any number greater than 1, you will get a false statement in the original inequality given to you.

Is this clear?