For the inequality x≤−3x≤−3 , which number(s) listed makes the inequality true? (Check ALL that apply!)(3 points) Responses -2.101101110... -2.101101110... -3.14 -3.14 −7–√−7negative square root of 7 -10.1010 -10.1010 −75/22
To solve the inequality x ≤ -3x ≤ -3, we can split it into two separate inequalities:
1. x ≤ -3x
2. -3x ≤ -3
1. For the inequality x ≤ -3x, we can simplify it by adding 3x to both sides:
4x ≤ 0
Dividing both sides by 4 gives:
x ≤ 0
2. For the inequality -3x ≤ -3, we can simplify it by dividing both sides by -3. When dividing by a negative number, we need to flip the inequality sign:
x ≥ 1
Now, we need to find which numbers satisfy both inequalities, x ≤ 0 and x ≥ 1.
Checking the given numbers:
-2.101101110... is greater than 0 and less than 1, so it does not satisfy the inequality.
-3.14 is less than 0, so it does not satisfy the inequality.
-7√7 is less than 0, so it does not satisfy the inequality.
-10.1010 is less than 0, so it does not satisfy the inequality.
-75/22 is less than 0, so it does not satisfy the inequality.
None of the given numbers satisfy both inequalities, so the answer is none of the listed numbers make the inequality true.