Questions: Solve the inequality. 3x + 2 < 3(x - 6) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is . (Type your answer in interval notation.) B. The solution set is ∅.

Solve the inequality. 3x + 2 < 3(x - 6) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is . (Type your answer in interval notation.) B. The solution set is ∅.
Transcript text: Solve the inequality. \[ 3 x+2<3(x-6) \] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is $\square$ . (Type your answer in interval notation.) B. The solution set is $\varnothing$.
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Solution

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Solution Steps

Step 1: Expand the right-hand side of the inequality

The given inequality is: 3x+2<3(x−6) 3x + 2 < 3(x - 6) First, expand the right-hand side: 3(x−6)=3x−18 3(x - 6) = 3x - 18 So the inequality becomes: 3x+2<3x−18 3x + 2 < 3x - 18

Step 2: Simplify the inequality

Subtract 3x3x from both sides to eliminate the 3x3x terms: 3x+2−3x<3x−18−3x 3x + 2 - 3x < 3x - 18 - 3x This simplifies to: 2<−18 2 < -18

Step 3: Analyze the result

The inequality 2<−182 < -18 is false. This means there is no value of xx that satisfies the original inequality.

Final Answer

The solution set is ∅\varnothing. Therefore, the correct choice is: B. The solution set is ∅ \boxed{\text{B. The solution set is } \varnothing}

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