Answered

Dive into the world of knowledge and get your queries resolved at IDNLearn.com. Join our knowledgeable community and access a wealth of reliable answers to your most pressing questions.

Solve the equation.

[tex]\[ 12(2k + 11) = 12(2k + 12) \][/tex]

Sagot :

GinnyAnsweridn
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.
Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. For clear and precise answers, choose IDNLearn.com. Thanks for stopping by, and come back soon for more valuable insights.