Question

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

Answer 1

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`