where would the plots be on a number line for both solutions for the solutions to the following equation?
Solve the equation. Graph the solution(s) if possible.
-4|s+9|=-24
To solve the equation, we can start by dividing both sides by -4, which gives:
|s + 9| = 6
There are two possible solutions for this equation, depending on the value of s + 9.
1) If s + 9 ≥ 0, then |s + 9| = s + 9.
In this case, the equation becomes:
s + 9 = 6
Subtract 9 from both sides:
s = -3
2) If s + 9 < 0, then |s + 9| = -(s + 9).
In this case, the equation becomes:
-(s + 9) = 6
Distribute the negative sign:
-s - 9 = 6
Add 9 to both sides:
-s = 15
Multiply both sides by -1 to solve for s:
s = -15
So the two solutions to the equation are s = -3 and s = -15.
On a number line, we can plot these solutions as points:
s = -3 would be located at -3 on the number line.
s = -15 would be located at -15 on the number line.