Questions: 3(4-x)+3x ≤ 16

3(4-x)+3x ≤ 16
Transcript text: $3(4-x)+3x \leq 16$
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Solution

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Solution Steps

To solve the inequality \(3(4-x) + 3x \leq 16\), we need to:

  1. Distribute the 3 inside the parentheses.
  2. Combine like terms.
  3. Isolate the variable \(x\) on one side of the inequality.
  4. Solve for \(x\).
Step 1: Distribute the 3 inside the parentheses

We start with the inequality: \[ 3(4 - x) + 3x \leq 16 \]

Distribute the 3: \[ 3 \cdot 4 - 3 \cdot x + 3x \leq 16 \] \[ 12 - 3x + 3x \leq 16 \]

Step 2: Combine like terms

Combine the terms involving \( x \): \[ 12 \leq 16 \]

Step 3: Analyze the inequality

The inequality \( 12 \leq 16 \) is always true. This means that the original inequality holds for all values of \( x \).

Final Answer

\(\boxed{x \in \mathbb{R}}\)

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