Questions: Solve the inequality. 3(x-1)/2 ≤ x-3

Solve the inequality. 3(x-1)/2 ≤ x-3
Transcript text: Solve the inequality. \[ \frac{3(x-1)}{2} \leq x-3 \]
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Solution

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Solution Steps

To solve the inequality \(\frac{3(x-1)}{2} \leq x-3\), we can follow these steps:

  1. Clear the fraction by multiplying both sides by 2.
  2. Simplify the resulting expression.
  3. Isolate \(x\) on one side of the inequality.
  4. Solve for \(x\).
Step 1: Clear the Fraction

Multiply both sides of the inequality by 2 to eliminate the fraction: \[ 3(x-1) \leq 2(x-3) \]

Step 2: Simplify the Expression

Distribute and simplify both sides: \[ 3x - 3 \leq 2x - 6 \]

Step 3: Isolate \(x\)

Subtract \(2x\) from both sides: \[ x - 3 \leq -6 \]

Add 3 to both sides: \[ x \leq -3 \]

Final Answer

The solution to the inequality is: \[ \boxed{x \leq -3} \]

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