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Question 132450: 6(x+3)-2(x+5)greater vthan or equal to 7(x+1)-2
Answer by nycsharkman(136)   (Show Source):
You can put this solution on YOUR website! 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?
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