Please help 30 points. Don't put bad answers and show your work please.

Answer:

A) -4

Step-by-step explanation:

There are two ways of solving this:

1.) Plugging in the answer choices

Since the equation needs to be equal to or less than 1 (this is due to the less than or equal to sign:  ≤)

You will then set the equation: -2x-6 ≤ 1

You will then take each answer choice and plug it into the original equation.

Plug in -4:  -2(-4)-6 ≤ 1   this will result in 2 ≤ 1

Plug in -3:   -2(-3)-6 ≤ 1 this will result in 0 ≤ 1

Plug in -2:   -2(-2)-6 ≤ 1 this will result in -2 ≤ 1

Plug in -1:     -2(-1)-6 ≤ 1 this will result in -4≤ 1

The only one that is not true is when you plug in x=-4 into the equation -2x-6.  This results in the equation being equal to 2.  2 is not less than 1, making the equation false.

Method 2: Solving the inequality

You can essentially solve for x like a normal inequality.

Instead of solving for -2x-6 = 1, we are doing -2x-6 ≤ 1.

First: Add 6 to the right side

-2x ≤ 1+6 --->>>>  2x ≤ 7

Second:  Divid both sides by -2

***Note: When you divivde by a negative when solving an inequality, you must switch the sign. ***

x ≥ -3.5   (hence the sign swtiches from ≤ to ≥ since we divided by a negative value in the equation)

x ≥ -3.5 states that any number greater or equal to -3.5 will work.  -4 is less than -3.5, thus it will not satisfy the inequality.

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