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Step 1: [tex]\(3x - 8 = 2x + 23\)[/tex]

Step 2: [tex]\(x - 8 = 23\)[/tex]

Step 3: [tex]\(x = 31\)[/tex]

All of Jaiden's work is correct. The solution is [tex]\(x = 31\)[/tex].

In step 1, Jaiden incorrectly set the expressions equal to each other instead of adding them together and setting the total equal to [tex]\(90^\circ\)[/tex].

To get to step 2, Jaiden incorrectly subtracted [tex]\(2x\)[/tex] from both sides instead of adding [tex]\(2x\)[/tex] to both sides.

To get to step 3, Jaiden incorrectly added 8 to both sides instead of subtracting 23 from both sides.

Sagot :

GinnyAnsweridn
Let's carefully analyze and correct the mistakes mentioned in Jaiden's work.

### Step-by-Step Solution:

#### Problem:
Jaiden starts with the equation:
[tex]\[ 3x - 8 = 2x + 23 \][/tex]

Jaiden's steps:
1. Subtracted [tex]\(2x\)[/tex] from both sides to get:
[tex]\[ x - 8 = 23 \][/tex]
2. Added 8 to both sides to get:
[tex]\[ x = 31 \][/tex]

We need to address the original misunderstanding and solve the corrected problem.

#### Correction:
1. Identify the correct relationship and write the equation:

The problem states that the two expressions being dealt with should add up to [tex]\(90^\circ\)[/tex]. Therefore, the correct equation should be:
[tex]\[ (3x - 8) + (2x) = 90 \][/tex]

2. Simplify the equation:
[tex]\[ 3x - 8 + 2x = 90 \][/tex]
Combine like terms:
[tex]\[ 5x - 8 = 90 \][/tex]

3. Solve for [tex]\(x\)[/tex]:
a. Add 8 to both sides:
[tex]\[ 5x - 8 + 8 = 90 + 8 \][/tex]
[tex]\[ 5x = 98 \][/tex]

b. Divide both sides by 5:
[tex]\[ x = \frac{98}{5} \][/tex]

So, the correct value for [tex]\(x\)[/tex] is:
[tex]\[ x = \frac{98}{5} \][/tex]

### Final Remark:
Jaiden's initial approach had errors in forming and manipulating the equation. The correct solution after rectifying these steps is:
[tex]\[ x = \frac{98}{5} \][/tex]

This translates to:
[tex]\[ x = 19.6 \][/tex]

This is the detailed step-by-step solution explaining the errors and showing the correct method to solve the problem.
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