To determine whether [tex]\( x = 5 \)[/tex] is a solution to the equation [tex]\( 2x + 13 = 26 \)[/tex], we need to substitute [tex]\( x = 5 \)[/tex] into the equation and see if both sides of the equation are equal. Let's go through the steps:
1. Substitute [tex]\( x = 5 \)[/tex] into the equation:
[tex]\[
2(5) + 13
\][/tex]
2. Perform the multiplication:
[tex]\[
10 + 13
\][/tex]
3. Add the numbers:
[tex]\[
23
\][/tex]
So, when [tex]\( x = 5 \)[/tex], the left side of the equation [tex]\( 2x + 13 \)[/tex] evaluates to 23.
4. Compare the left side to the right side:
The original equation is:
[tex]\[
2x + 13 = 26
\][/tex]
Substituting [tex]\( x = 5 \)[/tex] gives us:
[tex]\[
23
\][/tex]
The right side of the equation was originally 26.
Since 23 does not equal 26, we can conclude that:
[tex]\[
x = 5 \quad \text{is not a solution to the equation} \quad 2x + 13 = 26.
\][/tex]
In summary, substituting [tex]\( x = 5 \)[/tex] into the equation [tex]\( 2x + 13 = 26 \)[/tex] results in the left side being 23, which does not match the right side of 26. Therefore, [tex]\( x = 5 \)[/tex] does not satisfy the equation.
