MATH SOLVE

2 months ago

Q:
# Solve the following equations, and check for extraneous solutionsa)(x-8)/(x-4)=2b)(4x-8)/(x-2)=4

Accepted Solution

A:

Answer:a) x = 0 is the solution to the equation.b) x = any real number except 2Step-by-step explanation:Hi there!a) First, let´s write the equation:(x-8) / (x-4) = 2Now let´s solve it for x. Let´s start subtracting 2 to both sides of the equation[(x-8) / (x-4)] - 2 = 0Let´s subtract both terms, the least common multiple is (x-4) [x-8 - 2(x - 4)] / (x-4) = 0Apply distributive property(x - 8 - 2x + 8) / (x - 4) = 0-x / (x-4) = 0x = 0Now, let´s check the solution: (x-8) / (x-4) = 2x = 00-8 / 0-4 = 2-8/-4 = 22 = 2Then x = 0 is the solution to the equation.b) Let´s write the equation:(4x-8)/(x-2)=4 Let´s proceed in the same way as in a)Subtract 4 to both sides of the equation.(4x-8)/(x-2) - 4 = 0 Subtract both terms[4x - 8 - 4(x-2)] / (x-2) = 0Apply distributive property(4x -8 - 4x + 8) / (x -2) = 00/(x-2) = 0x can be any real number except 2 because it would make the denominator zero.