Question

A. Solve the following Equations: a) |𝑥 − 6| = 3 b) |𝑥 − 4| = |−3𝑥 + 8| c) |2𝑥 + 4| = |5𝑥 + 2|

Answer 1

$|x-6|=3\implies \text{$x-6=3$ or $x-6=-3$}\\\text{Therefore, $x=9$ or x=3} \\|x-4|=|-3x+8|\\\text{Squaring both sides of the equation, we have}\\x^2-8x+16=9x^2-48x+64\\=-8x^2+40-48=0\\\text{Using factorization method, we have}\\(x-2)(x-3)=0\implies \text{x=2 or x=3} \\|2x+4|=|5x+2| \\\text{Squaring both sides of the equation, we have}\\4x^2+16x+16=25x^2+20x+4\\=-21x^2-4x-12=0\\\text{Using formula method, we have that}\\x=\frac{4\pm\sqrt{16-(4(-21)(12)}}{2(-21)}\\\implies \text{$x=-0.8571$ or $0.6667$}$