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slayer8001

  • one year ago

Solve the inequality 2x - 3 < x + 2 ≤ 3x + 5. Show your work.

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  1. slayer8001
    • one year ago
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    @peachpi

  2. slayer8001
    • one year ago
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    plz I really need help

  3. anonymous
    • one year ago
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    break this up. Do this one first \[2x-3 < x + 2\]

  4. slayer8001
    • one year ago
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    is it -1x<2x ?

  5. slayer8001
    • one year ago
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    @peachpi

  6. anonymous
    • one year ago
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    |dw:1441890766597:dw|

  7. anonymous
    • one year ago
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    then do \(x+2 \le 3x+5\)

  8. anonymous
    • one year ago
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    start by subtracting 3x from both sides

  9. slayer8001
    • one year ago
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    it would be the same wouldn't it?

  10. anonymous
    • one year ago
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    usually not.

  11. slayer8001
    • one year ago
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    is it -2+2<5?

  12. slayer8001
    • one year ago
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    after subtracting 3

  13. anonymous
    • one year ago
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    where did your x go? You should have -2x + 2 < 5 Then subtract the 2 from both sides

  14. slayer8001
    • one year ago
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    oops yeah forgot to put the x

  15. slayer8001
    • one year ago
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    -2x<3?

  16. anonymous
    • one year ago
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    right then divide by -2 and flip the sign since it's negative

  17. slayer8001
    • one year ago
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    -1x>0.67?

  18. anonymous
    • one year ago
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    x > -0.67 b/c you only flip once you divide by the negative

  19. anonymous
    • one year ago
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    also, you should leave it as \(x>-\frac{2}{3}\) because it's more exact

  20. slayer8001
    • one year ago
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    ok

  21. anonymous
    • one year ago
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    If you were to graph the two solutions it would look like this|dw:1441891511708:dw|

  22. anonymous
    • one year ago
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    But your final answer combines them|dw:1441891692074:dw|

  23. anonymous
    • one year ago
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    So the solution is all numbers between -2/3 and 5, including 5 and you'd write it as \[-\frac{ 2 }{ 3 }<x\le5\]

  24. slayer8001
    • one year ago
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    ok thanks so much I really appreciate your help

  25. anonymous
    • one year ago
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    you're welcome

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