Question:
The set of all \(x\) satisfying the inequality \(8 + 3x > 4(x - 3) + 2\) is
The set of all \(x\) satisfying the inequality \(8 + 3x > 4(x - 3) + 2\) is
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Remember that if you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality sign. Here, we avoided this by moving the smaller coefficient of \(x\) to the other side.
Updated On: Jun 24, 2026
- \((18, \infty)\)
- \((20, \infty)\)
- \((-\infty, 18)\)
- \((-\infty, 20)\)
- \((-20, 18)\)
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept:
To solve a linear inequality, we isolate the variable \(x\) on one side by performing algebraic operations similar to solving an equation.
Step 2: Key Formula or Approach:
Distribute constants, collect \(x\) terms on one side, and constants on the other.
Step 3: Detailed Explanation:
The inequality is:
\[ 8 + 3x > 4(x - 3) + 2 \]
Step 1: Expand the right side:
\[ 8 + 3x > 4x - 12 + 2 \]
Step 2: Simplify the right side:
\[ 8 + 3x > 4x - 10 \]
Step 3: Subtract \(3x\) from both sides:
\[ 8 > x - 10 \]
Step 4: Add 10 to both sides:
\[ 18 > x \]
This can be written as \(x < 18\). In interval notation, this represents the set \((-\infty, 18)\).
Step 4: Final Answer:
The solution set is \((-\infty, 18)\).
To solve a linear inequality, we isolate the variable \(x\) on one side by performing algebraic operations similar to solving an equation.
Step 2: Key Formula or Approach:
Distribute constants, collect \(x\) terms on one side, and constants on the other.
Step 3: Detailed Explanation:
The inequality is:
\[ 8 + 3x > 4(x - 3) + 2 \]
Step 1: Expand the right side:
\[ 8 + 3x > 4x - 12 + 2 \]
Step 2: Simplify the right side:
\[ 8 + 3x > 4x - 10 \]
Step 3: Subtract \(3x\) from both sides:
\[ 8 > x - 10 \]
Step 4: Add 10 to both sides:
\[ 18 > x \]
This can be written as \(x < 18\). In interval notation, this represents the set \((-\infty, 18)\).
Step 4: Final Answer:
The solution set is \((-\infty, 18)\).
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