What are the solutions of the inequality?
−2(3x+2)≥−6x−4
A.
x≥0
B.
x≤6
C.
all real numbers
D.
no solution
−2(3x+2)≥−6x−4
-6x - 4 ≥ -6x - 4
0 ≥ 0
which is true, so C
To find the solutions of the given inequality, we need to simplify and isolate the variable on one side of the inequality sign.
Let's start by distributing the -2 on the left side of the inequality:
-2(3x+2) ≥ -6x - 4
Simplifying this, we get:
-6x - 4 ≥ -6x - 4
Now, let's combine like terms:
-6x - 4 ≥ -6x - 4
We see that both sides of the inequality are identical. This means that no matter what value of x we choose, both sides will always be equal. Therefore, the inequality has infinitely many solutions, which means the answer is option C: all real numbers.