Question

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

Answer 1

Given

|2c+8|=|10c|

Find

Solve the equation

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

$\begin{gathered} 2c+8=-10c \\ 2c+10c=-8 \\ 12c=-8 \\ c=-\frac{8}{12} \\ \\ c=-\frac{2}{3} \end{gathered}$

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

c = 1

$\begin{gathered} |2c+8|=|10c| \\ |2\times1+8|=|10\times1| \\ \lvert10\rvert=\lvert10\rvert \end{gathered}$

it is true.

c = -2/3

$\begin{gathered} |2c+8|=|10c| \\ |2\times(-\frac{2}{3})+8|=|10\times(-\frac{2}{3})| \\ \\ |-\frac{4}{3}+8|=|-\frac{20}{3}| \\ \\ |\frac{-4+24}{3}|=|-\frac{20}{3}| \\ \\ |-\frac{20}{3}|=|-\frac{20}{3}| \end{gathered}$

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