Question

Help with math?

Answer 1

|x+3| +7 less than or equal to 10
Describe the graph of the solution in a complete sentence.

Answer 2

you can write it this way
|x+3| + 7 <= 10 (use <= if you can't type ≤ )

the first step is add -7 to both sides
|x+3| + 7 -7 <= 10-7
and simplify. 7-7 is 0 on the left side. 10-7 is 3. you get
|x+3|≤ 3

now that you have just an absolute value sign on the left side, we can write it as two different equations:
1) x+3 is positive, so the | | do nothing: x+3 ≤ 3
add -3 to both sides, simplify, and get x ≤3

2) x+3 is negative. the | | will make it positive. This is the same as saying multiply by -1:
-1(x+3) ≤ 3

distribute the -1 (multiply each term inside the parens by -1)
-x - 3 ≤ 3
add +x to both sides
-3 ≤ x - 3
add + 3 to both sides
0 ≤ x

you have the two solutions:
0 ≤ x
x ≤3

when says: x greater than or equal to zero, and less than or equal to 3
(all the numbers from 0 up to 3)

you can also write the answer as
0 ≤ x ≤ 3