Answered

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A student is asked to find the solution to this equation:

[tex]\[ 2x - 6 = 12 \][/tex]

The student's work is shown:

[tex]\[ 2x - 6 = 12 + 6 \][/tex]
[tex]\[ 2x = 18 \][/tex]
[tex]\[ x = \frac{18}{2} = 9 \][/tex]

The student's equation is [incorrect/correct] because it is [incorrectly/correctly solved].

One way we know this is [explanation].

Sagot :

GinnyAnswer
The student's equation is an incorrect equation because it is incorrectly solved.

One way we know this is that adding 6 to both sides of the equation should result in 18 on the right-hand side, not 12.

Let's go through the correct step-by-step solution to the equation \(2x - 6 = 12\):

1. Start with the given equation:
[tex]\[ 2x - 6 = 12 \][/tex]

2. Add 6 to both sides of the equation:
[tex]\[ 2x - 6 + 6 = 12 + 6 \][/tex]

3. Simplify both sides:
[tex]\[ 2x = 18 \][/tex]

4. Divide both sides by 2 to solve for \(x\):
[tex]\[ \frac{2x}{2} = \frac{18}{2} \][/tex]

5. Simplify the expression:
[tex]\[ x = 9 \][/tex]

This shows that the correct solution to the equation [tex]\(2x - 6 = 12\)[/tex] is [tex]\(x = 9\)[/tex].
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