Sure, let's verify whether [tex]\( x = 3 \)[/tex] is a solution to the equation [tex]\( 2x + 5 = 11 \)[/tex].
1. Substitute [tex]\( x = 3 \)[/tex] into the left-hand side of the equation:
The given equation is [tex]\( 2x + 5 = 11 \)[/tex].
2. Calculate the left-hand side (LHS) with [tex]\( x = 3 \)[/tex]:
Substitute [tex]\( x = 3 \)[/tex] into [tex]\( 2x + 5 \)[/tex]:
[tex]\[
2(3) + 5
\][/tex]
Simplify the expression:
[tex]\[
6 + 5 = 11
\][/tex]
3. Compare the result with the right-hand side (RHS) of the equation:
The right-hand side of the equation is 11.
4. Verify if the left-hand side (LHS) equals the right-hand side (RHS):
From our calculations, we find that:
[tex]\[
2(3) + 5 = 11
\][/tex]
Since:
[tex]\[
11 = 11
\][/tex]
5. Conclusion:
Since the left-hand side (11) is equal to the right-hand side (11), [tex]\( x = 3 \)[/tex] satisfies the equation [tex]\( 2x + 5 = 11 \)[/tex]. Therefore, [tex]\( x = 3 \)[/tex] is indeed a solution to the equation.
