Let's solve the equation step-by-step:
Given the equation:
[tex]\[ 12(2k + 11) = 12(2k + 12) \][/tex]
1. Distribute the 12 on both sides:
Left-hand side (LHS):
[tex]\[ 12 \cdot (2k + 11) = 12 \cdot 2k + 12 \cdot 11 = 24k + 132 \][/tex]
Right-hand side (RHS):
[tex]\[ 12 \cdot (2k + 12) = 12 \cdot 2k + 12 \cdot 12 = 24k + 144 \][/tex]
So, the equation becomes:
[tex]\[ 24k + 132 = 24k + 144 \][/tex]
2. Isolate the variable term:
Subtract [tex]\( 24k \)[/tex] from both sides:
[tex]\[ 24k + 132 - 24k = 24k + 144 - 24k \][/tex]
[tex]\[ 132 = 144 \][/tex]
3. Analyze the resulting equation:
The resulting statement, [tex]\( 132 = 144 \)[/tex], is a contradiction. This means there is no value of [tex]\( k \)[/tex] that will satisfy the initial equation.
Thus, the equation has no solutions. The solution set is the empty set, which indicates that there are no values for [tex]\( k \)[/tex] that make the original equation true.
