Test Session Unit 5: Linear Equations and Inequalities (9th Mathematics)

Mathematics (SNC) – Class 9th

Q1. Choose the correct option.

Solution of $5 x - 10 = 10$ 5x−10=10 is:
(C) $x = 4$ x=4
A vertical line divides the plane into:
(D) Two half planes
$3 x + 4 < 0$ 3x+4<0 is:
(B) Inequality
Solve and represent the solution of $12 x + 30 = - 6$ 12x+30=−6:
(B) $x = - 3$ x=−3
The solution of $\frac{x}{2} - 1 \leq 0$ 2x−1≤0 on the real line:
(A) $x \leq 2$ x≤2
Solution of $\frac{2 x - 3}{5} \geq 3$ 52x−3≥3:
(B) $x \geq 9$ x≥9
The line $- 3, - 2, - 1, 0, 1, 2$ −3,−2,−1,0,1,2 represents:
(C) $- 3 \leq x \leq 2$ −3≤x≤2
Value of $x$ x in $\frac{x + 3}{2} = \frac{x - 4}{3}$ 2x+3=3x−4:
(B) $x = - 17$ x=−17
For what value of $x$ x is $x^{2} - 6 x + 8 \leq 0$ x2−6x+8≤0 true?
(C) $2 \leq x \leq 4$ 2≤x≤4
Solution set of $x + y \geq 5$ x+y≥5 and $- y + x \leq 1$ −y+x≤1:
(D) $x = 3, y = 2$ x=3,y=2

Q2. Short Answers

[i] $x = 3$ x=3
[ii] $x = - 5$ x=−5
[iii] $x \geq 1$ x≥1
[iv] $x < 2$ x<2
[v] $x \geq 0.4$ x≥0.4
[vi] $x \leq 3$ x≤3
[vii] $x \geq - 1$ x≥−1
[viii] $x < 3$ x<3
[ix] $x > 2$ x>2
[x] Linear Equation: Equation of the form $a x + b = 0$ ax+b=0. Example: $2 x + 3 = 7$ 2x+3=7
[xi] (i) $x = 4$ x=4, (ii) $x = - 6$ x=−6
[xii] $x = - 1$ x=−1
[xiii] Shade region below line $5 x - 4 y = 20$ 5x−4y=20 including the line
[xiv] Shade region satisfying $4 x - 3 y \leq 12$ 4x−3y≤12 and $x \geq - \frac{3}{2}$ x≥−23
[xv] $x = - 18$ x=−18

Q3. Detailed Answers (Answer any 2)

1. Shade solution region for 3x−2y≥63x−2y≥6

Find boundary line: $3 x - 2 y = 6$ 3x−2y=6
Intercepts: $x = 2$ x=2 (y=0), $y = - 3$ y=−3 (x=0)
Test point (0,0): $0 \geq 6$ 0≥6 → False
Shade region below the line (not including origin)

✅ Graph: Line solid, region below shaded.

2. Shade solution region for 5x−4y≤205x−4y≤20

Boundary: $5 x - 4 y = 20$ 5x−4y=20
Intercepts: $x = 4$ x=4 (y=0), $y = - 5$ y=−5 (x=0)
Test (0,0): $0 \leq 20$ 0≤20 → True
Shade region above the line (including origin)

✅ Graph: Line solid, region above shaded.

3. Shade solution for 3x+7y≥213x+7y≥21 and x−y≤2x−y≤2

First line: $3 x + 7 y = 21$ 3x+7y=21 → Intercepts (7,0) & (0,3)
Test (0,0): $0 \geq 21$ 0≥21 → False → Shade opposite side
Second line: $x - y = 2$ x−y=2 → Intercepts (2,0) & (0,-2)
Test (0,0): $0 \leq 2$ 0≤2 → True → Shade same side as origin
Final region: Intersection of both shaded areas

✅ Graph: Overlapping region in first quadrant and above.