Question

Solve the equation and check your solution.|2c+8|=|10c|

Answer 1

Given

|2c+8|=|10c|

Find

Solve the equation

Step-by-step explanation

as we have given absolute value equation

|2c+8|=|10c| ,.

there are 2 possibility , either

`2c+8=10c,2c+8=-10c`

now we solve both cases .,

1. ) 2c + 8 = 10c

`\begin{gathered} 2c+8=10c \\ 2c-10c=-8 \\ -8c=-8 \\ c=1 \end{gathered}`

2 ) 2c + 8 = -10c

`\begin{gathered} 2c+8=-10c \\ 2c+10c=-8 \\ 12c=-8 \\ c=-(8)/(12) \\ \\ c=-(2)/(3) \end{gathered}`

for checking the solution , we need to put these c values in given equation .,

c = 1

`\begin{gathered} |2c+8|=|10c| \\ |2*1+8|=|10*1| \\ \lvert10\rvert=\lvert10\rvert \end{gathered}`

it is true.

c = -2/3

`\begin{gathered} |2c+8|=|10c| \\ |2*(-(2)/(3))+8|=|10*(-(2)/(3))| \\ \\ |-(4)/(3)+8|=|-(20)/(3)| \\ \\ |(-4+24)/(3)|=|-(20)/(3)| \\ \\ |-(20)/(3)|=|-(20)/(3)| \end{gathered}`

it also holds.

so , the solutions are 1 and -2/3

Final Answer

Therefore , the solution of this equation are c = 1 and c = -2/3