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Solve for [tex]$x$[/tex]: [tex]$8x - 2 - 5x = 8$[/tex]

A. [tex][tex]$x = 13$[/tex][/tex]

B. [tex]$x = \frac{21}{2}$[/tex]

C. [tex]$x = \frac{31}{3}$[/tex]

D. [tex][tex]$x = 7$[/tex][/tex]


Sagot :

To solve the equation [tex]\( 8x - 2 - 5x = 8 \)[/tex], follow these steps:

1. Combine like terms on the left side of the equation:

[tex]\( 8x \)[/tex] and [tex]\( -5x \)[/tex] are like terms. Subtract [tex]\( 5x \)[/tex] from [tex]\( 8x \)[/tex]:

[tex]\[ 8x - 5x = 3x \][/tex]

Now substitute back into the equation:

[tex]\[ 3x - 2 = 8 \][/tex]

2. Isolate the term containing [tex]\( x \)[/tex]:

To isolate [tex]\( 3x \)[/tex], add 2 to both sides of the equation:

[tex]\[ 3x - 2 + 2 = 8 + 2 \][/tex]

Simplify:

[tex]\[ 3x = 10 \][/tex]

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

Divide both sides of the equation by 3 to solve for [tex]\( x \)[/tex]:

[tex]\[ x = \frac{10}{3} \][/tex]

The value of [tex]\( x \)[/tex] is [tex]\( \frac{10}{3} \)[/tex].

4. Compare [tex]\( x \)[/tex] with the given options:
- Option A: [tex]\( 13 \)[/tex]
- Option B: [tex]\( \frac{21}{2} \)[/tex]
- Option C: [tex]\( \frac{31}{3} \)[/tex]
- Option D: [tex]\( 7 \)[/tex]

Convert the value [tex]\( \frac{10}{3} \)[/tex] to a decimal form for easier comparison:

[tex]\[ \frac{10}{3} \approx 3.3333 \][/tex]

After comparison with the options:
- Option A: 13 is incorrect.
- Option B: [tex]\( \frac{21}{2} = 10.5\)[/tex] is incorrect.
- Option C: [tex]\( \frac{31}{3} \approx 10.3333 \)[/tex] is incorrect.
- Option D: 7 is incorrect.

None of the provided options correctly matches [tex]\( x = \frac{10}{3} \)[/tex]. Therefore, there is no correct option given in the list provided.