Solve the absolute value equation. | S - 54.4 | < 15.5
To solve the absolute value equation |S - 54.4| < 15.5, we can break it down into two separate cases:
1. S - 54.4 < 15.5
In this case, we solve for S:
S < 15.5 + 54.4
S < 69.9
2. -(S - 54.4) < 15.5
First, we remove the negative sign by multiplying both sides by -1:
S - 54.4 > -15.5
Next, we solve for S:
S > -15.5 + 54.4
S > 38.9
So the solution to the absolute value equation |S - 54.4| < 15.5 is 38.9 < S < 69.9.
To solve the absolute value equation |S - 54.4| < 15.5, we need to remove the absolute value by considering two cases: one where the expression inside the absolute value is positive and one where it is negative.
Case 1: S - 54.4 is positive:
If S - 54.4 is positive, the equation |S - 54.4| < 15.5 can be rewritten as S - 54.4 < 15.5. To solve this equation, we isolate S by adding 54.4 to both sides: S < 15.5 + 54.4. Simplifying this, we get S < 69.9.
Case 2: S - 54.4 is negative:
If S - 54.4 is negative, the equation |S - 54.4| < 15.5 can be rewritten as -(S - 54.4) < 15.5. To solve this equation, we isolate S by multiplying both sides by -1. Be sure to switch the direction of the inequality when multiplying by a negative number: S - 54.4 > -15.5. Adding 54.4 to both sides, we get S > -15.5 + 54.4. Simplifying this, we get S > 38.9.
Thus, combining both cases, we have the solution: 38.9 < S < 69.9.
To solve the absolute value equation |S - 54.4| < 15.5, we need to consider two cases:
Case 1: S - 54.4 > 0
In this case, the absolute value |S - 54.4| can be rewritten without the absolute value symbols. Therefore, the equation becomes:
S - 54.4 < 15.5
To isolate S, we can add 54.4 to both sides of the equation:
S - 54.4 + 54.4 < 15.5 + 54.4
S < 69.9
Case 2: S - 54.4 < 0
In this case, the absolute value |S - 54.4| becomes -(S - 54.4), and the inequality changes direction. Therefore, the equation becomes:
-(S - 54.4) < 15.5
To simplify the equation, we distribute the negative sign:
-S + 54.4 < 15.5
Next, we can isolate S by subtracting 54.4 from both sides of the equation:
-S + 54.4 - 54.4 < 15.5 - 54.4
-S < -38.9
Since we multiplied both sides of the inequality by -1, we need to reverse the inequality sign:
S > 38.9
Combining the solutions from both cases, the solution to the absolute value equation |S - 54.4| < 15.5 is:
38.9 < S < 69.9