Verified Answer :

  • Divide both sides of the equation \(6(x+20) = 168\) by 6 to obtain \(x + 20 = 28\).
  • Subtract 20 from both sides to solve for \(x\), yielding \(x = 8\).
  • Match the result with the given options to find that B is the correct choice.
  • Final answer: \(\boxed{B}\)

Explanation

  1. Analysis and Planning

We are given the linear equation:
\[6(x+20) = 168\]
Our goal is to solve for the variable \(x\). We have a few approaches here: we can either distribute the 6 across the terms in the parentheses or divide both sides of the equation by 6 to isolate the expression \((x + 20)\) first. Dividing by 6 is often more efficient as it simplifies the numbers immediately.

  1. Isolating the Variable Term

To isolate \((x + 20)\), we divide both sides of the equation by 6:
\[x + 20 = \frac{168}{6}\]
Performing the division:
\[\frac{168}{6} = 28\]
So, the equation simplifies to:
\[x + 20 = 28\]

  1. Solving for x and Selecting the Option

Now, we isolate \(x\) by subtracting 20 from both sides:
\[x = 28 - 20\]
\[x = 8\]
Comparing this result with the given options:

A\(x = 4 \frac{2}{3}\)
B\(x = 8\)
C\(x = 24 \frac{2}{3}\)
D\(x = 28\)

The correct option is B.

Examples

Imagine you are managing a small warehouse and you have 6 boxes, each containing an unknown number of items \(x\) plus 20 extra units in a special divider. If the total number of items across all 6 boxes is 168, the equation \(6(x + 20) = 168\) helps you determine that each box contains \(x = 8\) items. This type of algebraic modeling is essential for inventory management and resource allocation.

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