Alright, let's solve the equation step-by-step:
The given equation is:
[tex]\[ 8x - (2x - 13) = 36 \][/tex]
Step 1: Simplify inside the parentheses
First, we distribute the negative sign inside the parentheses:
[tex]\[ 8x - 2x + 13 = 36 \][/tex]
Step 2: Combine like terms
Next, we combine the [tex]\( x \)[/tex] terms:
[tex]\[ (8x - 2x) + 13 = 36 \][/tex]
[tex]\[ 6x + 13 = 36 \][/tex]
Step 3: Isolate the variable [tex]\( x \)[/tex]
To isolate [tex]\( x \)[/tex], we need to get rid of the constant term on the left side. Subtract 13 from both sides of the equation:
[tex]\[ 6x + 13 - 13 = 36 - 13 \][/tex]
[tex]\[ 6x = 23 \][/tex]
Step 4: Solve for [tex]\( x \)[/tex]
Now, divide both sides of the equation by 6 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{23}{6} \][/tex]
So, the solution to the equation is:
[tex]\[ x = \frac{23}{6} \][/tex]
Step 5: Verify the solution
To ensure our solution is correct, we can plug [tex]\( x = \frac{23}{6} \)[/tex] back into the original equation and check if the left side equals the right side:
[tex]\[ 8 \left( \frac{23}{6} \right) - \left( 2 \left( \frac{23}{6} \right) - 13 \right) = 36 \][/tex]
Calculate each term:
[tex]\[ 8 \left( \frac{23}{6} \right) = \frac{184}{6} \][/tex]
[tex]\[ 2 \left( \frac{23}{6} \right) = \frac{46}{6} \][/tex]
[tex]\[ \frac{46}{6} - 13 = \frac{46}{6} - \frac{78}{6} = -\frac{32}{6} \][/tex]
[tex]\[ \frac{184}{6} - \left( -\frac{32}{6} \right) = \frac{184}{6} + \frac{32}{6} = \frac{216}{6} = 36 \][/tex]
Both sides are equal, which means our solution is correct.
Therefore, the correct choice is:
[tex]\[ \boxed{\{ \frac{23}{6} \}} \][/tex]
