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2. What is the value of [tex]$x$[/tex] in the equation [tex]\frac{x-2}{3} + \frac{1}{6} = \frac{5}{6}[/tex]?

A. 4
B. 6
C. 8
D. 11


Sagot :

To find the value of [tex]\( x \)[/tex] in the equation

[tex]\[ \frac{x-2}{3} + \frac{1}{6} = \frac{5}{6} \][/tex]

we need to solve step-by-step. Let's break it down:

1. Eliminate the fractions: To simplify the equation, we can multiply every term by 6 (the common denominator) to clear the fractions.

[tex]\[ 6 \left( \frac{x-2}{3} \right) + 6 \left( \frac{1}{6} \right) = 6 \left( \frac{5}{6} \right) \][/tex]

2. Simplify each term:

- For the first term:

[tex]\[ 6 \left( \frac{x-2}{3} \right) = 2(x - 2) \][/tex]

- For the second term:

[tex]\[ 6 \left( \frac{1}{6} \right) = 1 \][/tex]

- For the third term:

[tex]\[ 6 \left( \frac{5}{6} \right) = 5 \][/tex]

3. Re-write the equation with the simplified terms:

[tex]\[ 2(x - 2) + 1 = 5 \][/tex]

4. Distribute and simplify further:

- Distribute the 2 in the first term:

[tex]\[ 2x - 4 + 1 = 5 \][/tex]

- Combine like terms:

[tex]\[ 2x - 3 = 5 \][/tex]

5. Solve for [tex]\( x \)[/tex]:

- Add 3 to both sides of the equation:

[tex]\[ 2x - 3 + 3 = 5 + 3 \][/tex]

- Simplify the equation:

[tex]\[ 2x = 8 \][/tex]

- Divide both sides by 2 to isolate [tex]\( x \)[/tex]:

[tex]\[ x = \frac{8}{2} \][/tex]

- Simplify:

[tex]\[ x = 4 \][/tex]

Therefore, the value of [tex]\( x \)[/tex] is 4. The correct answer is:

A. 4