SOLUTION: Given the following inequality: -4(x-3)+ 5 <= 3x-7 (<= means the line underneath) a. find the solution set for x b. verify answer by checking on value inside the solution set

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Question 117844: Given the following inequality: -4(x-3)+ 5 <= 3x-7 (<= means the line underneath)
a. find the solution set for x
b. verify answer by checking on value inside the solution set and one value outside the solution set
c. How does the answer change in the above equation change if we change the <= to a =.
Thank you
Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website!
You can work these using the rules you apply to equations ... with the exception that if you
multiply or divide both sides by a negative quantity, you reverse the direction of the inequality
sign.
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Given:
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a) Find the solution set:
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First do the distributed multiplication on the left side by multiplying -4 times each of
the two terms in the parentheses. The multiplication leads to:
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On the left side combine the +12 and +5 to get +17. This reduces the equation to:
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Get rid of the +17 on the left side by subtracting 17 from both sides:
.

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Finally, get rid of the 3x on the right side by subtracting 3x from both sides:
.

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To solve for +x, divide both sides by -7, the multiplier of x. Don't forget that since you are
dividing both sides by a negative quantity, you must reverse the direction of the inequality
sign. The division by -7 reduces the problem to:
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and the division on the right side results in:
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x can be any value equal to or greater than +24/7
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b) Check ... suppose we let x be zero ... a value that is less than 24/7. Since this is outside
the solution set, the inequality should not be correct.
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Start with:
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Setting x equal to zero results in:
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This is not true ... +17 is not less than or equal to -7. So this checks.
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Now let's set x equal to +4. Because 4 is greater than 24/7, the inequality should work.
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Start with:
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Substitute +4 for x and it becomes:
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Combine the terms in the parentheses to get:
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Do the multiplications ... one on the left side and one on the right side:
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Combine the terms on the left side and also combine the terms on the right side.
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This is true because 5 is greater than 1. So the inequality works for 1 value of x that is
greater than 24/7.
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c) How does the answer change if the inequality/equal sign is changed to an = sign.
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The only thing this does is to change the inequality sign to an equal sign in the answer. With
the equal sign in the problem the answer is just .
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Hope this helps you to better understand the process of solving inequalities.
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