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Question 88910: I could use some help thank you
Solve and graph the solution set. 4x + 8 >= 3x + 16
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! As long as you remember the rule that if you MULTIPLY OR DIVIDE both sides of an inequality
by a MINUS quantity, you REVERSE the direction of the inequality sign, you can work these
problems just as you would an equation. You will not use this rule in this problem,
but you may need to use it in other problems you are assigned.
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You are given:
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4x + 8 >= 3x + 16
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To collect the terms containing x on the left side, begin by subtracting 3x from both sides.
When you do that subtraction the 3x disappears from the right side and the equation
becomes:
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4x - 3x + 8 >= 16
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Combine the x terms on the left side (4x - 3x) to get x, and the equation becomes:
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x + 8 >= 16
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Get rid of the 8 on the left side by subtracting 8 from both sides to end up with:
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x >= 8
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To graph this, draw the number line and put a filled dot where x equals +8. This tells you
that x equals +8. But x can be any number greater than +8 also. So make the number line
to the right of x = +8 a very heavy line. This combination, the filled dot at +8 and the
very heavy line to the right of that dot all the way to positive infinity indicates
that x can be any value starting at 8 and going all the way to the right from that point.
.
Hope this helps you to understand the problem and how to graph inequalities on the number
line.
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