(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Instructions: For the following inequalities, determine if 0 is a number in the solution set.

1) 3x [tex]\leq[/tex] x+1 [tex]\leq[/tex] x-1

2) x(2x-1) [tex]\leq[/tex] x+7

2. Relevant equations

3. The attempt at a solution

1)

LS:

[tex]3x \leq x+1 [/tex]

[tex]3x-1 \leq x [/tex]

[tex]-1 \leq -3x [/tex]

[tex]-1/-2 \geq -2x/-2[/tex]

[tex]1/2 \geq x [/tex]

RS:

[tex]x+1 \leq x-1[/tex]

[tex]0 \leq -2[/tex]

I said for the right side that there are no solutions, since the inequality is not true.

So I said that 0 is not included in the solution set in this inequality, based from the inequality from the left side.

2)

[tex] x(2x-1) \leq x+7 [/tex]

[tex] 2x^2 - x \leq x+7 [/tex]

[tex] 2x^2 - 2x - 7 \leq 0 [/tex]

After that I tried factoring the equation. It would work, just not with even numbers though...have some decimals on it.

This is what I tried so far for both questions.

Note: I looked at the wrong part of the question, that's why I changed the question, but its still the same equations.

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# Homework Help: Solving double inequalities

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