How many solutions does the equation |𝟸𝚡 + 𝟻| + 𝟷𝟸 = 𝟺 have?

Answer 1

Kyrah, remember that absolute value is the distance from zero. Since we measure distance in positive numbers (even if you back up 5 feet, you still travelled 5 feet), absolute value is always positive.

-10 and 10 are both 10 away from 0, so that's why both have an absolute value of 10.

Usually, when we solve an equation like this, we'd have to set what is inside the absolute value sign to both positive and negative, for the reason stated above.

|2x - 5| = 5

2x - 5 = 5

Solve for x.

And, since -5 also has an absolute value of 5...

2x - 5 = -5

Solve for x.

Now, with the given problem...

|2x + 5| + 12 = 4

|2x + 5| = -8

Well, as we know, absolute value is ALWAYS positive, so we can't have an absolute value of anything be -8. Therefore, there are no solutions.

Hope this helps.

Answer 2

|𝟸𝚡 + 𝟻| + 𝟷𝟸 = 𝟺

|𝟸𝚡 + 𝟻| = 𝟺 - 12 = -8

|𝟸𝚡 + 𝟻| = -8 ?

Is it possible that the absolute function gives a negative value?