Algebra (Please help!)

Hey! I've been having a lot of trouble with this, please help!

x - 7 > 10
x > __

3x < 20 (underscore under the less / greater than sign)
x < __

5a - 2 < 8
a < __

2t + 8 > 4(t + 1) (underscore under the less/greater than sign)
t > __

asked by Carolyn
  1. I assume you want to solve these inequalities. Just do them the way you would work with equations.

    x - 7 > 10
    add 7 to both sides:
    x > 17

    3x <= 20
    divide by 3:
    x <= 20/3

    5a - 2 < 8
    add 2, then divide by 5:
    5a < 10
    a < 2

    2t + 8 >= 4(t + 1)
    2t + 8 >= 4t + 4
    subtract 4 and subtract 2t:
    4 >= 2t
    2 >= t
    or, t <= 2

    posted by Steve
  2. If you know how to solve equations, you should have no trouble solving inequations.
    Just pretend you have an equal sign and use the same steps.
    The only exception is: When you multiply or divide both sides by a negative number, you must also reverse the inequality sign

    I will do the last one to illustrate

    2t + 8 ≥ 4(t + 1)
    2t + 8 ≥ 4t + 4 , same as you would for equation
    2t -4t ≥ 4 - 8 , same as you would for equation
    -2t ≥ -4, still the same steps , BUT NOW:
    I have to divide by -2, so do the arithmetic for that
    but, I have to reverse the inequality sign

    t ≤ 2

    check my answer by taking a value of x below 2, then another above 2 in the original inequation.
    notice at t = 2, the left side equals the right side

    you do the others the same way

    posted by Reiny
  3. Thank you both so much! This helps a lot :)

    posted by Carolyn

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