Bright Tutorials Bright Tutorials
ICSE Class 10 Mathematics Question 16 of 21

Solved 2024 Question Paper ICSE Class 10 Mathematics — Question 10

Back to all questions
10
Question

Question 7(ii)

Solve the following inequation, write down the solution set and represent it on the real number line.

-3 + x ≤ 7x2+2\dfrac{7x}{2} + 2 < 8 + 2x, x ∈ I.

Answer

Given,

-3 + x ≤ 7x2+2\dfrac{7x}{2} + 2 < 8 + 2x

Solving L.H.S. of the above inequation :

⇒−3+x≤7x2+2⇒7x2−x≥−3−2⇒7x−2x2≥−5⇒5x2≥−5⇒x≥−5×25⇒x≥−2 ..........(1)\Rightarrow -3 + x \le \dfrac{7x}{2} + 2 \\[1em] \Rightarrow \dfrac{7x}{2} -x \ge -3 - 2 \\[1em] \Rightarrow \dfrac{7x - 2x}{2} \ge -5 \\[1em] \Rightarrow \dfrac{5x}{2} \ge -5 \\[1em] \Rightarrow x \ge \dfrac{-5 \times 2}{5} \\[1em] \Rightarrow x \ge -2 \text{ ..........(1)}

Solving R.H.S. of the above inequation :

⇒7x2+2<8+2x⇒7x2−2x<8−2⇒7x−4x2<6⇒3x2<6⇒x<6×23⇒x<4 ..........(2)\Rightarrow \dfrac{7x}{2} + 2 \lt 8 + 2x \\[1em] \Rightarrow \dfrac{7x}{2} - 2x \lt 8 - 2 \\[1em] \Rightarrow \dfrac{7x - 4x}{2} \lt 6 \\[1em] \Rightarrow \dfrac{3x}{2} \lt 6 \\[1em] \Rightarrow x \lt \dfrac{6 \times 2}{3} \\[1em] \Rightarrow x \lt 4 \text{ ..........(2)}

From inequation (1) and (2), we get :

-2 ≤ x < 4.

Since, x ∈ I.

x = {-2, -1, 0, 1, 2, 3}.

Solve the following inequation, write down the solution set and represent it on the real number line. ICSE 2024 Maths Solved Question Paper.

Hence, solution set = {-2, -1, 0, 1, 2, 3}.