If P is the solution set of -3 x -4-2 x -3- x - N andQ is the solution set of 4 x -5-12- x - W- find Q - P-4 MARKS-

Solving inequation P and Q: 1.5 Marks each Answer: 1 Mark 3x +4 lt;2x 3, xϵ N ⇒ 5x lt; 7 ⇒ x gt;7/5 x=2,3,4... ⇒ P=2,3,4... Now, 4x 5 lt;12,x ϵ W ⇒ ...

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Standard X

Mathematics

Solving a Quadratic Equation by Factorization Method

If P is the s...

Question

If P is the solution set of $- 3 x + 4 < 2 x - 3, x ϵ N$ and
Q is the solution set of $4 x - 5 < 12, x ϵ W$ , find Q-P.
[4 MARKS]

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Solution

Solving inequation P and Q: 1.5 Marks each
Answer: 1 Mark

$- 3 x + 4 < 2 x - 3, x ϵ N$
$\Rightarrow - 5 x < - 7 \Rightarrow x > \frac{7}{5} x = 2, 3, 4... \Rightarrow P = 2, 3, 4...$
Now, $4 x - 5 < 12, x ϵ W \Rightarrow 4 x < 17 \Rightarrow x < \frac{17}{4}, x = 1, 2, 3, 4 \Rightarrow Q = 0, 1, 2, 3, 4$
$Q - P = 0, 1$

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If P is the solution set of −3x+4<2x−3,xϵN and Q is the solution set of 4x−5<12,xϵW, find Q-P. [4 MARKS]

Solving inequation P and Q: 1.5 Marks each Answer: 1 Mark −3x+4<2x−3,xϵN ⇒−5x<−7⇒x>75x=2,3,4...⇒P=2,3,4... Now, 4x−5<12,xϵW⇒4x<17⇒x<174,x=1,2,3,4⇒Q=0,1,2,3,4 Q−P=0,1

If P is the solution set of $- 3 x + 4 < 2 x - 3, x ϵ N$ and
Q is the solution set of $4 x - 5 < 12, x ϵ W$ , find Q-P.
[4 MARKS]