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Question 997705: How do you do multi step inequalities?
Answer by addingup(3677)   (Show Source):
You can put this solution on YOUR website! Do you have a specific equation you need to solve? IF so, you should post it. But I'll give you three examples you can use, find a few inequalities so you can practice, just follow my steps.
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Example 1:
4x+3 < -1 Subtract 3 from both sides:
4x < -4 Divide both sides by 4:
x < -1
You can write it in interval notation:
(-infinite, -1) from negative infinity to -1 but not including -1 If it was including -1 we would use a bracket ] and not a parenthesis )
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Example 2:
5x > 8x+27 Subtract 8x from both sides:
-3x > 27 Now divide both sides by -3 and remember that when you divide or multiply an inequality by a negative number you change the sign, like this:
-3x/-3 < 27/-3 Calculate and you get:
x < -9
In interval notation:
(-infinite, -9) Again, it's an inequality so we use a parenthesis to indicate that it goes up to -9 but without including -9.
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Example 3:
8x-5(4x+1) ≥ -1+2(4x-3)
8x-20x-5 ≥ -1+8x-6 Let's simplify by adding/subtracting on both sides:
-12x-5 ≥ -7+8x Now let's subtract 8x and add 5 to both sides:
-20x ≥ -2 Now let's divide both sides by -20, and remember, when we divide or multiply both sides of an inequality by a negative number we have to change the sign:
x= ≤ -2/-20 Now, on the right you have -/- and you know what happens when you either multiply or divide two negatives, right? - and - = +. So we simplify and rewrite:
x ≤ 1/10
In interval notation:
(-infinite, 1/10] (because it's an equal or smaller, the 1/10 is included)
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