Basic Mathematics & Logarithm
System of linear inequalities
Grade 11
Question:
<p>Solution of \(4x+3\geq 2x+17\), \(3x-5<-2\) linear inequalities is</p>
<p>\(x\geq 7\)</p>
<p>\(x<1\)</p>
<p>\(1>x\geq 7\)</p>
<p>not possible</p>
Step-by-Step Solution
Key Concept: Solve each linear inequality separately, then find the intersection of solution sets. The final answer must satisfy both inequalities simultaneously.
<p><strong>Step 1:</strong> Solve the first inequality: 4x + 3 ≥ 2x + 17</p><p>4x - 2x ≥ 17 - 3</p><p>2x ≥ 14</p><p>x ≥ 7</p><p><strong>Step 2:</strong> Solve the second inequality: 3x - 5 < x + 7</p><p>3x - x < 7 + 5</p><p>2x < 12</p><p>x < 6</p><p><strong>Step 3:</strong> Find the intersection of both conditions: x ≥ 7 AND x < 6</p><p>Since no value can be simultaneously ≥ 7 and < 6, the solution set is empty.</p><p>∴ Answer: D (Empty set / No solution / ∅)</p>
Correct Answer: D