Question

Solve 2x-7 ≤ 3 (1-x) for real values.​

Answer 1

Answer:

y=

x

2

+2x−7

x

2

+34x−71

yx

2

+2xy−7y=x

2

+34x−71

x

2

(1−y)+2x(17−y)+7y−71=0x∈R

4(17−y)

2

−4(1−y)(7y−71)≥0

4(17

2

+y

2

−34y)−4(−7y

2

−71+78y)≥0

⇒8y

2

−112y+360≥0

⇒y

2

−14y+45≥0

⇒(y−9)(y−5)≥0

y∈(−∞,5)∪(9,∞)

Answer 2

$= 2x-7 ≤ 3 (1-x)$

$= 2x-7 ≤ 3 - 3x$

$= 2x + 3x ≤ 3 + 7$

$= 5x ≤ 10$

$= x ≤ \frac{10}{5}$

$x = \: ≤ 2$

$Solution \: Set =(−∞,2)$