Question

solve the modulus equations below. (a) |2x+3|=6. (b) |x-2|=x+4. (c) |2x-7|=|x+3|​

Answer 1

Answer:

(a) x=1.5 or  x=-4.5

(b) x=-1

(c) x=10  or  $x=\frac{4}{3}$

Step-by-step explanation:

(a) |2x+3|=6

⇒ 2x+3=6  or  2x+3=-6

⇒ 2x=3 or  2x=-9

⇒ x=1.5 or  x=-4.5

(b) |x-2|=x+4

⇒ x-2=x+4  or  x-2=-(x+4)

x-2=x+4  

-2≠4 x∈Ф

or  x-2=-(x+4)

x-2=-x-4

2x=-2

x=-1

(c) |2x-7|=|x+3|​

⇒ 2x-7=x+3  or  2x-7=-(x+3)

2x-7=x+3

x=10

or  2x-7=-(x+3)

2x-7=-x-3

3x=4

$x=\frac{4}{3}$