Solve and check the equation. [tex]\[ 8x - (2x - 13) = 36 \][/tex]
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is [tex]\(\{ \} \)[/tex]. (Type an integer or a simplified fraction.) B. The solution set is [tex]\(\{ x \mid x \text{ is a real number} \} \)[/tex]. C. The solution set is [tex]\(\varnothing\)[/tex].
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]
