Solve the system of inequalities- x-5-7x-2- 4x-9- 2x-3-7x-5- 3x-9-

The correct option is A 4≤ x ≤ 1 (x+5) 7(x 2)≥ 4x+9 ⇒ x+5 7x+14≥ 4x+9 ⇒ 6x+19≥ 4x+9 Add 4x and 19 both sides, we get 6 ...

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Byju's Answer

Standard XII

Mathematics

Manipulation of a linear equation

Solve the sys...

Question

Solve the system of inequalities: $(x + 5) - 7 (x - 2) \geq 4 x + 9, 2 (x - 3) - 7 (x + 5) \leq 3 x - 9$ .

- 4 \leq x \leq 1

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- 4 \leq x \leq 4

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- 1 \leq x \leq 1

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- 9 / 4 \leq x \leq 1

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Solution

The correct option is A $- 4 \leq x \leq 1$
$(x + 5) - 7 (x - 2) \geq 4 x + 9$
$\Rightarrow x + 5 - 7 x + 14 \geq 4 x + 9$
$\Rightarrow - 6 x + 19 \geq 4 x + 9$
Add $- 4 x$ and $- 19$ both sides, we get
$- 6 x + 19 - 4 x - 19 \geq 4 x + 9 - 4 x - 19$
$\Rightarrow - 6 x - 4 x \geq 9 - 19$
$\Rightarrow - 10 x \geq - 10$
Divided by $- 10$ , we get
$x \leq 1$
Also,
$2 (x - 3) - 7 (x + 5) \leq 3 x - 9$
$\Rightarrow 2 x - 6 - 7 x - 35 \leq 3 x - 9$
$\Rightarrow - 5 x - 41 \leq 3 x - 9$
Add $- 3 x$ and $- 41$ both sides, we get
$- 5 x - 41 - 3 x + 41 \leq 3 x - 9 - 3 x + 41$
$\Rightarrow - 5 x - 3 x \leq - 9 + 41$
$\Rightarrow - 8 x \leq 32$
Divided by $- 8$ both sides, we get
$x \geq - 4$
Then $- 4 \leq x \leq 1$

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Solve the system of inequalities: (x+5)−7(x−2)≥4x+9,2(x−3)−7(x+5)≤3x−9.

Solve the system of inequalities: $(x + 5) - 7 (x - 2) \geq 4 x + 9, 2 (x - 3) - 7 (x + 5) \leq 3 x - 9$ .