Given: −16 = m5−18 Prove: m = 10 Statements Reasons 1. −16 = m5−18 1. Given 2. 2=m5 2. Response area 3. 10 = m 3. Response area 4. m = 10
4. Conclusion from step 3 (substituting the value of m into the equation).
Proof:
1. -16 = m5 - 18 [Given]
2. 2 = m5 [Subtracted 18 from both sides]
3. Divide both sides by 5:
(2/5) = (m5)/5
2/5 = m [Divided both sides by 5]
4. Solving for m:
m = 2/5
Simplify:
m = 10/5
m = 2 [Simplified the fraction]
5. Therefore, m = 2 is not equal to m = 10, so the given equation -16 = m5 - 18 cannot be proven to be true.
To prove that m = 10 based on the equation −16 = m5−18, we need to go through the following steps:
1. Given the equation: −16 = m5−18
2. Subtract 5 from both sides of the equation: −16 + 5 = m5−18 + 5
- This simplifies to: −11 = m5−13
- The purpose of this step is to isolate m on one side of the equation.
3. Add 13 to both sides of the equation: −11 + 13 = m5−13 + 13
- This simplifies to: 2 = m5
- The purpose of this step is to further simplify the equation.
4. Divide both sides of the equation by 5: 2/5 = m5/5
- This simplifies to: 2/5 = m
- The purpose of this step is to isolate the value of m.
5. Simplify 2/5: 2/5 = m
- The value of 2/5 is equal to 0.4.
6. Therefore, m = 0.4.
Based on the calculations above, it appears that there was an error in the initial statement "m = 10" provided in the question. The correct solution, based on the given equation, is m = 0.4.