Question

1. (b-2b) quyida berilgan sonlardan qaysi biri $(x - 3)(x + 8) > 0$ tengsizlikning yechimi bo‘la oladi?

a) $x = -10$
b) $x = 0$
c) $x = -3$
d) $x = -6$

1. (b-2b) tenglamani yeching: $sqrt{4x - 3} = 5$

a) $x = \frac{11}{2}$
b) $x = 2$
c) $x = 7$
d) $x = \frac{1}{2}$

1. (q-2,6b) tenglamaning ildizini toping: $\frac{2x - 6}{x^2 - 4} = 0$

a) 3 va $-2$
b) 3
c) 3, $-2$ va 2
d) 3 va 2

1. (q-2,6b) a traktor 4 kunda 7 gektar, b traktor esa 5 kunda 13 gektar yerni shudgor qila oladi. fermer xo‘jaligida a traktordan 2 ta va b traktordan 1 ta bor. agar bu traktorfar birgalikda ishlatiltsa, fermer xo‘jaligining 122 gektar yerini necha kunda shudgor qiladi?

a) 18
b) 20
c) 16
d) 14

Explanation:

Question 3

Step1: Find critical points

Set \((x - 3)(x + 8)=0\), so \(x = 3\) or \(x=-8\). These divide the number line into intervals: \((-\infty,-8)\), \((-8,3)\), \((3,\infty)\).

Step2: Test intervals

• For \(x < -8\) (e.g., \(x=-10\)): \((-10 - 3)(-10 + 8)=(-13)(-2)=26>0\), so \(x=-10\) satisfies \((x - 3)(x + 8)>0\).
• For \(-8 < x < 3\) (e.g., \(x = 0\)): \((0 - 3)(0 + 8)=(-3)(8)=-24<0\), so \(x = 0\) does not satisfy.
• For \(x > 3\) (e.g., \(x = 4\)): \((4 - 3)(4 + 8)=(1)(12)=12>0\), but we check given options. Among options, \(x=-10\) is in the first interval.

Step1: Square both sides

Given \(\sqrt{4x - 3}=5\), square both sides: \(4x - 3 = 25\).

Step2: Solve for \(x\)

Add 3 to both sides: \(4x=28\), then divide by 4: \(x = 7\).

Step1: Set numerator to zero (for root)

For \(\frac{2x - 6}{x^2 - 4}=0\), numerator \(2x - 6 = 0\) gives \(x = 3\).

Step2: Check denominator

Denominator \(x^2 - 4
eq0\) (i.e., \(x
eq\pm2\)). So \(x = 3\) is the root (since \(x = 3\) does not make denominator zero).

Answer:

A. \(x = -10\)

Question 4