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I need help on this whole worksheet. I already did E and A and L

I need help on this whole worksheet. I already did E and A and L-example-1
User Spouk
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1 Answer

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Given:


8-2(2x+9)<42

Step 1:

Collect like terms

Thus, we have


\begin{gathered} -2(2x+9)<42-8 \\ -2(2x+9)<34 \end{gathered}

Step 2:

Open the brackets in the Left Hand Side of the inequality.


\begin{gathered} -2(2x+9)<34 \\ -2(2x)+(-2(9))<34 \\ \Rightarrow-4x-18<34 \end{gathered}

Step 3:

Collect like terms


\begin{gathered} -4x-18<34 \\ -4x<34+18 \\ -4x<52 \end{gathered}

Step 4:

Divide both sides of the inequality by the coefficient of x.

The coefficient of x is -4.

Thus,


\begin{gathered} (-4x)/(-4)<(52)/(-4) \\ \Rightarrow x>-13 \end{gathered}

When the coefficient of an unknown is a negative number, and is to be used to divide both sides of the inequality, the signs are changed.

Thus, the solution to the inequality is


x>-13

User Michael Benin
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