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.
