Answered

Jerome solved the equation [tex]\(\frac{1}{3} x + \frac{5}{6} = 1\)[/tex] as shown:

1. Subtraction property: [tex]\(\frac{1}{3} x + \frac{5}{6} - \frac{5}{6} = 1 - \frac{5}{6}\)[/tex]
2. LCD: [tex]\(\frac{1}{3} x = \frac{1}{6} - \frac{5}{6}\)[/tex]
3. Multiply by the reciprocal: [tex]\(\left(\frac{3}{1}\right) \frac{1}{3} x = \frac{-4}{6} \left(\frac{3}{1}\right)\)[/tex]
4. Solve and simplify: [tex]\(x = \frac{-12}{6} = -2\)[/tex]

Analyze Jerome's steps. In which step did he make an error?

A. In step 1, he needed to add [tex]\(\frac{5}{6}\)[/tex] to both sides of the equation.
B. In step 2, the LCD was not used correctly to make equivalent fractions.
C. In step 3, the correct reciprocal was not multiplied to both sides.
D. In step 4, the answer was not reduced correctly.



Answer :

GinnyAnswer
Let's carefully analyze Jerome's steps in solving the equation [tex]\(\frac{1}{3} x + \frac{5}{6} = 1\)[/tex].

1. Subtraction property:
Jerome applied the subtraction property correctly:
[tex]\[ \frac{1}{3} x + \frac{5}{6} - \frac{5}{6} = 1 - \frac{5}{6} \][/tex]
Simplifying the right side:
[tex]\[ \frac{1}{3} x = 1 - \frac{5}{6} \][/tex]
Since [tex]\(1\)[/tex] can be written as [tex]\(\frac{6}{6}\)[/tex]:
[tex]\[ 1 - \frac{5}{6} = \frac{6}{6} - \frac{5}{6} \][/tex]
This simplifies correctly to:
[tex]\[ \frac{1}{6} \][/tex]

2. LCD:
Jerome then correctly expressed the equation:
[tex]\[ \frac{1}{3} x = \frac{1}{6} \][/tex]

3. Multiply by the reciprocal:
Jerome attempted to isolate [tex]\(x\)[/tex] by multiplying both sides by the reciprocal of [tex]\(\frac{1}{3}\)[/tex], which is [tex]\(3\)[/tex]:
[tex]\[ \left(\frac{3}{1}\right) \cdot \frac{1}{3} x = \frac{1}{6} \cdot \left(\frac{3}{1}\right) \][/tex]
On the left side:
[tex]\[ \left(\frac{3}{1}\right) \cdot \frac{1}{3} x = x \][/tex]
On the right side:
[tex]\[ \frac{1}{6} \cdot 3 = \frac{3}{6} \][/tex]

4. Solve and simplify:
Jerome then simplified [tex]\(\frac{3}{6}\)[/tex]:
[tex]\[ x = \frac{3}{6} \][/tex]
However, Jerome incorrectly simplified this fraction. Instead of simplifying [tex]\(\frac{3}{6}\)[/tex] to [tex]\(\frac{1}{2}\)[/tex], he wrote it as [tex]\(x = -2\)[/tex].

Therefore, Jerome's error occurred in step 4 where he failed to correctly simplify the fraction [tex]\(\frac{3}{6}\)[/tex] to [tex]\(\frac{1}{2}\)[/tex].

The correct solution is:
[tex]\[ x = \frac{1}{2} \][/tex]

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