Answered

Given the inequality 6x ≤ 18, which of the following is a solution that makes the inequality true?


A{26}
B{14}
C{7}
D{3}

Verified Answer :

  • Simplify the inequality \(6x \le 18\) by dividing both sides by 6 to get \(x \le 3\).
  • Test each given option: \(x=6, 4, 7, 3\) to determine which satisfies the condition \(x \le 3\).
  • Conclude that only \(x=3\) makes the inequality true.
  • The final answer is \(\boxed{d}\).

Explanation

  1. Analyzing and Solving the Inequality

We are given the linear inequality \(6x \le 18\). To find the values of \(x\) that satisfy this inequality, we isolate \(x\) by dividing both sides of the inequality by \(6\). Since 6 is a positive number, the direction of the inequality sign remains unchanged.
\[x \le \frac{18}{6}\]
Performing the division, we obtain:
\[x \le 3\]
This inequality means that any real number \(x\) less than or equal to 3 is a solution.

  1. Testing the Given Options

Now we evaluate the provided options against our solution \(x \le 3\):

A\(x = 6\): Since \(6 > 3\), it is not a solution.
B\(x = 4\): Since \(4 > 3\), it is not a solution.
C\(x = 7\): Since \(7 > 3\), it is not a solution.
D\(x = 3\): Since \(3 \le 3\) is a true statement, it is a solution.

Therefore, the correct choice is d.

Examples

In real life, linear inequalities like this one are used in budgeting. For example, if you have a budget of \$18 for a product that costs \$6 per unit, the number of units \(x\) you can purchase must satisfy \(6x \le 18\). Solving this gives \(x \le 3\), meaning you can buy at most 3 units. This helps in making financial decisions by setting limits on resources.

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