$11-5 x>-4$ and $4 x+13 \leq-11$ $11-5 x>-4$ $11-5 x-11>-4-11$ $-5 x>-15$ Dividing both the sides by 5 we get, $-5 x / 5>-15 / 5$ $-x>-3$ $x<3$ $\therefore \mathrm{X}...
Solve each of the following system of equations in R- 
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Exercise 15.2
Solve each of the following system of equations in R-
Solve each of the following system of equations in R – 
$3 x-1 \geq 5$ and $x+2>-1$ $3 x-1 \geq 5$ $3 x-1+1>5+1$ $3 x \geq 6$ Dividing both the sides by 3 we get, $3 x / 3 \geq 6 / 3$ $x \geq 2$ $\therefore \mathrm{X} \in(2, \infty) \ldots(1)$ Now,...
Solve each of the following system of equations in R – 5x – 1 < 24, 5x + 1 > –24
$5 x-1<24$ and $5 x+1>-24$ $5 x-1<24$ $5 x-1+1<24+1$ $5 x<25$ Dividing both the sides by 5 we get, $5 x / 5<25 / 5$ $x<5$ $\therefore \mathrm{x} \in(-\infty, 5) \ldots(1)$ Now,...
Solve each of the following system of equations in R- 2x + 5 ≤ 0, x – 3 ≤ 0
$2 x+5 \leq 0$ and $x-3 \leq 0$ Let us consider the first inequality. $2 x+5 \leq 0$ $2 x+5-5 \leq 0-5$ $2 x \leq-5$ Dividing both the sides by 2 we get, 2x/2 ≤ –5/2 x ≤ – 5/2 ∴ x ∈ (–∞, -5/2]… (1)...
Solve each of the following system of equations in R- 2x – 3 < 7, 2x > –4
$2 x-3<7$ and $2 x>-4$ $2 x-3<7$ $2 x-3+3<7+3$ $2 \mathrm{x}<10$ Dividing both the sides by 2 we get, $2 x / 2<10 / 2$ $x<5$ $\therefore \mathrm{x} \in(-\infty, 5) \ldots(1)$...
Solve each of the following system of equations in R – 3x – 6 > 0, 2x – 5 > 0
$3 x-6>0$ and $2 x-5>0$ $3 x-6>0$ $3 x-6+6>0+6$ $3 x>6$ Dividing both the sides by 3 we get, $3 x / 3>6 / 3$ $x>2$ $\therefore \mathrm{x} \in(2, \infty) \ldots(1)$ Now, $2...
Solve each of the following system of equations in R- 2x + 6 ≥ 0, 4x – 7 < 0
$2 x+6 \geq 0$ and $4 x-7<0$ $2 x+6 \geq 0$ $2 x+6-6 \geq 0-6$ $2 x \geq-6$ Dividing both the sides by 2 we get, $2 x / 2 \geq-6 / 2$ $x \geq-3$ $\therefore \mathrm{x} \in[-3, \infty) \ldots(1)$...
Solve each of the following system of equations in R. x – 2 > 0, 3x < 18
$x-2>0$ and $3 x<18$ $x-2>0$ $x-2+2>0+2$ $x>2$ $\therefore \mathrm{X} \in(2, \infty) \ldots(1)$ Now, $3 x<18$ Dividing both the sides by 3 we get, $3 x / 3<18 / 3$...