First, let's make sure we understand the symbols:
In math, the straight bars, (in this case |d-3|) are not parenthesis, they have a different meaning.
Straight bars represent the "absolute value" of (whatever is inside of them).
The arrow with a line under it (depending on which way the arrow is facing) signifies "less or equal to" or "greater or equal to."
Also ... although you didn't specifically ask about the symbols, I wanted to make sure we are on the same page ... sort of speak.
So ... again:
|x| means absolute
value of x
≤ means less than or equal to
≥ means greater than or equal to
As of solving the problem, this is what you do:
1 - Break down the problem into these 2 equations:
d + 3 ≥ 7
- (d + 3) ≥ 7
2 - Solve the first equation:
d + 3 ≥ 7
First, Subtract 3 from both sides
d ≥ 7 - 3
Second, simplify 7−3 to 4
d ≥ 4
3 - Solve the 2nd equation:
First, simplify brackets
− d − 3 ≥ 7
Second, add 3 to both sides
- d ≥ 7 + 3
Third, simplify 7 + 3 to 10
- d ≥ 10
Fourth, multiply both sides by -1
d ≤ − 10
4 - Collect all solutions
d ≥ 4
d ≤ − 10
Remember, since you are working with absolute values, there will be more than one solution (answers) to the problem.