Question

Solve the equation for x; |x + 2| = 2(3 - x)​

Answer 1

Answer:

x+2=2(3-x)

x+2=6-2x

x+2x=6-2

3x=4

x=4/3

Answer 2

$\huge\tt{\red{\underline{Given:}}}$

★$|x+2|=2(3-x)$

$\huge\tt{\red{\underline{To\:\:Find:}}}$

★The value of x.

$\huge\tt{\red{\underline{Concept\:\:Used:}}}$

★We will square both sides to remove modulus.

$\huge\tt{\red{\underline{Answer:}}}$

We have,

$\implies |x+2|=2(3-x)$

$\implies (|x+2|)^{2}=[2(3-x)]^{2}$

$\implies (x+2)^{2}=2^{2}(3-x)^{2}$

$\implies x^{2}+4+4x=4(9+x^{2}-6x)$

$\large\green{\boxed{(a+b)^{2}=a^{2}+b^{2}+2ab}}$

$\large\green{\boxed{(a-b)^{2}=a^{2}+b^{2}-2ab}}$

$\implies\small{x^{2}+4+4x=36+4x^{2}-24x}$

$\implies 4x^{2}-x^{2}-24x-4x+36-4=0$

$\implies 3x^{2}-28x+32=0$

On factorising,

$\implies 3x^{2}-24x-4x+32=0$

$\implies 3x(x-8) -4(x-8) =0$

$\implies (3x-4) (x-8) =0$

${\underline{\boxed{.°. x =8, \dfrac{4}{3}}}}$