Solve the equation. Check for extraneous solutions. 2|7-7x|=2x+4

Question

Solve the equation. Check for extraneous solutions.


`2|7-7x|=2x+4`

Answer 1

2(7-7x) = 2x + 4
14 - 14x = 2x +4
16x = 10
x = 10/16
x = 0.625


2[-(7-7x)] = 2x + 4
-14 +14x = 2x + 4
12x = 18
x = 18/12
x = 1.5

answer:
solutions x = 0.625 and x = 1.5

Answer 2

Answer: The answer is
`(5)/(8),~(3)/(2)` and no extraneous solution.

Step-by-step explanation: The given equation is

`2|7-7x|=2x+4.`

We are given to solve this equation and also find its extraneous solution.

The solution is as follows:

`2|7-7x|=2x+4\\\\\Rightarrow |7-7x|=x+2\\\\\Rightarrow 7-7x=x+2,~~~~~-7+7x=x+2\\\\\Rightarrow 8x=5,~~~~~~~~~~~~~~~~\Rightarrow 6x=9\\\\\\\Rightarrow x=(5)/(8),~~~~~~~~~~~~~~~~~\Rightarrow x=(3)/(2).`

now, for
`x=(5)/(8)`, we have

`L.H.S.=2|7-7* (5)/(8)|=(21)/(4),\\\\R.H.S.=2*(5)/(8)+4=(21)/(4).`

So, this solution is not extraneous.

For
`x=(3)/(2)`, we have

`L.H.S.=2|7-7* (3)/(2)|=7,\\\\R.H.S.=2*(3)/(2)+4=7.`

So, this solution is also not extraneous.

Hence, the solution is [tex]\dfrac{5}{8},~\dfrac{3}{2}[tex] and there is no extraneous solution.