Question

solve |x/3 + 2/5| =2

Answer 1

Hint:

x/3 + 2/5 = 2
x/3 + 2/5 = -2

Answer 2

why is it positive AND negative 2? doesn't absolute value make it positive only? @Hero

Answer 3

I'll explain by demonstration:

|2| = 2
|-2| = 2

Answer 4

Notice that with absolute value, there are two values of which the absolute value is 2

Answer 5

So it makes sense that there are two equations that can represent this situation.

Answer 6

oh okay, i forgot about that rule, thanks! so i did both of the equations you hinted and got 24/5 and -36/5 :O

Answer 7

ill type out my work, just give me a minute :)

Answer 8

Typing out your work is always the best thing to do.

Answer 9

\[\frac{5}{5}*\frac{x}{3}+\frac{2}{5}*\frac{3}{3}=2\]
\[\frac{5(x)}{15}+\frac{2(3)}{15}=2\]
\[\frac{5x}{15}+\frac{6}{15}=2\]
\[\frac{15}{1}*\frac{5x+6}{15}=2*\frac{15}{1}\]
\[5x+6=30\]
\[5x=24\]
\[x=\frac{24}{5}\]

Answer 10

Yes, that's correct.

Answer 11

\[\frac{5}{5}*\frac{x}{3}+\frac{2}{5}*\frac{3}{3}=-2\]
\[\frac{5x}{15}+\frac{6}{15}=-2\]
\[5x+6=-30\]
\[5x=-36\]
\[x=\frac{-36}{5}\]

Answer 12

thank you so much for checking and helping me! i appreciate it :)

Answer 13

You can always check your work:

Notice that:

\[\frac{\frac{24}{5}}{3} + \frac{2}{5}\]
\[\frac{24}{5}\frac{1}{3} + \frac{2}{5}\]
\[\frac{24}{15} + \frac{6}{15} = \frac{30}{15} = 2\]

Answer 14

oh wow, i didn't know that was how to check the work! thanks that really helps! :)

Answer 15

Of course if you used -36/5 in place of x, you would end up with -2. But then the absolute value of -2 is 2 so it checks out :)