Question

Solve the equation. Check for extraneous solutions. rmula1" title="2|7-7x|=2x+4 " alt="2|7-7x|=2x+4 " align="absmiddle" class="latex-formula">

Answer 1

Answer: The answer is $\dfrac{5}{8},~\dfrac{3}{2}$ 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:

$2|7-7x|=2x+4\\\\\Rightarrow |7-7x|=x+2\\\\\Rightarrow 7-7x=x+2,~~~~~-7+7x=x+2\\\\\Rightarrow 8x=5,~~~~~~~~~~~~~~~~\Rightarrow 6x=9\\\\\\\Rightarrow x=\dfrac{5}{8},~~~~~~~~~~~~~~~~~\Rightarrow x=\dfrac{3}{2}.$

now, for $x=\dfrac{5}{8}$, we have

$L.H.S.=2|7-7\times \dfrac{5}{8}|=\dfrac{21}{4},\\\\R.H.S.=2\times\dfrac{5}{8}+4=\dfrac{21}{4}.$

So, this solution is not extraneous.

For $x=\dfrac{3}{2}$, we have

$L.H.S.=2|7-7\times \dfrac{3}{2}|=7,\\\\R.H.S.=2\times\dfrac{3}{2}+4=7.$

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.

Answer 2

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