Here is a detailed, step-by-step solution for solving the equation [tex]\( -7x + 25 = 48 \)[/tex]:
1. Original Equation:
[tex]\[
-7x + 25 = 48
\][/tex]
2. Isolate the term involving [tex]\( x \)[/tex]:
To do this, we need to get rid of the constant term on the left side. We can do this by subtracting 25 from both sides of the equation.
[tex]\[
-7x + 25 - 25 = 48 - 25
\][/tex]
Simplifying both sides:
[tex]\[
-7x = 23
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
Now that we have isolated the term involving [tex]\( x \)[/tex], we can solve for [tex]\( x \)[/tex] by dividing both sides of the equation by [tex]\( -7 \)[/tex]:
[tex]\[
x = \frac{23}{-7}
\][/tex]
Simplifying:
[tex]\[
x = -3.2857142857142856
\][/tex]
Identifying the Error in Jordan's Solution:
In Jordan's solution, the error occurs in Step 3.
- Jordan should have divided both sides by [tex]\( -7 \)[/tex], but instead, he divided by [tex]\( 7 \)[/tex]. The correct approach is:
[tex]\[
\frac{-7x}{-7} = \frac{23}{-7}
\][/tex]
Which simplifies to:
[tex]\[
x = -3.2857142857142856
\][/tex]
Error Identification Summary:
- Jordan incorrectly divided by [tex]\( 7 \)[/tex] in Step 3.
- Jordan should have divided both sides by [tex]\( -7 \)[/tex].
After identifying the error and following the correct steps, we verified that [tex]\( x = -3.2857142857142856 \)[/tex] is indeed the solution to the equation [tex]\( -7x + 25 = 48 \)[/tex].
