- Thread starter harpazo
- Start date

\(\displaystyle | x + 20| = 0.75 \)

\(\displaystyle (x + 20) =0.75 \)

\(\displaystyle x + 20 = 0.75 \)

\(\displaystyle x + 20 - 20 = 0.75 - 20\)

\(\displaystyle x = -19.25\)

Check

\(\displaystyle |(-19.25) + 20| = 0.75\)

\(\displaystyle |0.75| = 0.75\)

Negative side:

\(\displaystyle | x + 20| = 0.75 \)

\(\displaystyle -(x + 20) = 0.75 \)

\(\displaystyle -x - 20 = 0.75 \)

\(\displaystyle -x - 20 + 20 = 0.75 + 20 \)

\(\displaystyle -x = 20.75\)

\(\displaystyle \dfrac{x}{-1} = \dfrac{20.75}{-1}\)

\(\displaystyle x = -20.75\)

Check

\(\displaystyle |(-20.75) + 20| = 0.75\)

\(\displaystyle |-0.75| = 0.75\)

Two solutions of \(\displaystyle -19.25, -20.75\)

Do we always get two solutions?

\(\displaystyle | x + 20| = 0.75 \)

\(\displaystyle (x + 20) =0.75 \)

\(\displaystyle x + 20 = 0.75 \)

\(\displaystyle x + 20 - 20 = 0.75 - 20\)

\(\displaystyle x = -19.25\)

Check

\(\displaystyle |(-19.25) + 20| = 0.75\)

\(\displaystyle |0.75| = 0.75\)

Negative side:

\(\displaystyle | x + 20| = 0.75 \)

\(\displaystyle -(x + 20) = 0.75 \)

\(\displaystyle -x - 20 = 0.75 \)

\(\displaystyle -x - 20 + 20 = 0.75 + 20 \)

\(\displaystyle -x = 20.75\)

\(\displaystyle \dfrac{x}{-1} = \dfrac{20.75}{-1}\)

\(\displaystyle x = -20.75\)

Check

\(\displaystyle |(-20.75) + 20| = 0.75\)

\(\displaystyle |-0.75| = 0.75\)

Two solutions of \(\displaystyle -19.25, -20.75\)

Not sure. I would say so because of the structure of it.Do we always get two solutions?

\(\displaystyle |ax+b|=c\) where \(0<c\) and \(a\ne0\)

\(\displaystyle ax+b=\pm c\)

\(\displaystyle x=\frac{-b\pm c}{a}\)

If \(c=0\), then we get one solution, and if \(c<0\) we get no solution.

Can you share an example when c = 0 and when c < 0?

\(\displaystyle |ax+b|=c\) where \(0<c\) and \(a\ne0\)

\(\displaystyle ax+b=\pm c\)

\(\displaystyle x=\frac{-b\pm c}{a}\)

If \(c=0\), then we get one solution, and if \(c<0\) we get no solution.