Question
19. Show that 1.27 is not a solution for the equation \( g+3.74=5.1 \). Then the correct solution and show why it is correct.
Ask by Murray Phillips. in the United States
Mar 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( g = 1.36 \) is the correct solution because when substituted back into the equation \( g + 3.74 = 5.1 \), it satisfies the equation.
Solution
**Step 1. Test the proposed solution**
Substitute \( g = 1.27 \) into the equation:
\[
1.27 + 3.74 = 5.01
\]
Since \( 5.01 \neq 5.1 \), \( 1.27 \) is not a solution.
---
**Step 2. Solve the equation correctly**
Starting with the equation:
\[
g + 3.74 = 5.1
\]
Subtract \( 3.74 \) from both sides to isolate \( g \):
\[
g = 5.1 - 3.74
\]
Calculate the difference:
\[
g = 1.36
\]
Thus, the correct solution is \( g = 1.36 \).
---
**Step 3. Verify the correct solution**
Substitute \( g = 1.36 \) back into the original equation:
\[
1.36 + 3.74 = 5.1
\]
Since the left-hand side equals the right-hand side, the solution \( g = 1.36 \) is verified as correct.
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Mind Expander
To show that 1.27 is not a solution for the equation \( g + 3.74 = 5.1 \), we can substitute \( g \) with 1.27: \[ 1.27 + 3.74 = 5.01 \] Since 5.01 does not equal 5.1, we confirm that 1.27 is not the correct value for \( g \). Now, let's solve for \( g \) correctly. To isolate \( g \), we subtract 3.74 from both sides of the equation: \[ g = 5.1 - 3.74 \] \[ g = 1.36 \] This is correct because when we plug 1.36 back into the original equation: \[ 1.36 + 3.74 = 5.1 \] The equation holds true, confirming that 1.36 is indeed the solution.
