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Today, 02:17

Choose the correct description of the graph of the compound inequality

3x + 2 > 2 and 3x less than 6.

A number line with an open circle on 0, shading to the left, and a closed circle on 2, shading to the right.

A number line with a closed circle on 0, shading to the left, and an open circle on 2, shading to the right.

A number line with a closed circle on 0, an open circle on 2, and shading in between.

A number line with an open circle on 0, a closed circle on 2, and shading in between.

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Answers (2)
  1. Today, 03:17
    0
    The correct answer is:

    A number line with an open circle on 0, an open circle on 2, and shading in between. (This was not listed as a choice.)

    Explanation:

    Our first inequality is 3x+2 > 2.

    To solve this, first subtract 2 from each side:

    3x+2-2 > 2-2

    3x > 0

    Divide both sides by 3:

    3x/3 > 0/3

    x > 0

    The second equation is "3x less than 6." This translates to

    3x < 6

    Divide both sides by 3:

    3x/3 < 6/3

    x < 2

    This makes our answer "x > 0 and x < 2." This can also be written as

    0 < x < 2.

    To graph this, draw a number line. The numbers must range so that 0 and 2 are on it.

    Draw open circles on 0 and 2. The circles are open because the signs are strictly greater than and strictly less than; there is no "greater than or equal to" or "less than or equal to."

    Since the numbers are greater than 0 and less than 2, this means the number line between them will be shaded.
  2. Today, 04:12
    0
    We are given with two inequalities

    3x + 2 > 2 (eqn 1) 3x < - 6 (eqn 2)

    in eqn 1, we transpose 2 to the right side, then3x > 0, x > 0in eqn 2, we divide the whole equation by 3, that is x<-2

    Thus the domain is. D. A number line with an open circle on 0, a closed circle on 2, and shading in between.
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