Algebra

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Solve the system of inequalities.

y<2x+4
-3x - 2y> 6

So I just want y alone. For the second inequality, I added 3x to both sides and got -2y> 3x+6. Then I divided both sides by -2. I got y> -3/2 - 3
Do I have to switch the inequality symbol or something?

  • Algebra -

    whenever you multiply/divide by a negative value, the direction of the inequality changes. It's just a shorthand for moving things to the other side. For example,

    -2x < 8
    0 < 8+2x
    -8 < 2x
    -4 < x
    or, just dividing by -2 and switching the direction,
    x > -4

    So, for your problem,

    -3x - 2y> 6
    -3x-6 > 2y
    y < -3/2 x - 3

    Also, we have
    y < 2x+4

    So, to satisfy both equations,
    find where the two lines intersect. The solution set is points where y is below both lines.

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