the absolute value of x plus 7. Or in other words, we must have.

of something and I got you 1/7, there's two possible things that out, and that was intentional.

So, we must have.

If one side does not contain an absolute value then we need to look at the two potential answers and make sure that each is in fact a solution. This case looks very different from any of the previous problems we’ve worked to this point and in this case the formula we’ve been using doesn’t really work at all.

We're just subtracting

In the case the quantities inside the absolute value were the same number but opposite signs. In this definition we are going to think of \(\left| p \right|\) as the distance of \(p\) from the origin on a number line. call it, the thing that's multiplying the absolute times the absolute value of x plus 7.

In other words, we can’t get a negative value out of the absolute value. Note as well that we also have \(\left| 0 \right| = 0\).

So, all together there is a single solution to this equation : \[x = \frac{1}{4}\]. Absolute Value Absolute Value means ..... only how far a number is from zero: "6" is 6 away from zero, and "−6" is also 6 away from zero.

Now, let’s check \(x = - 5\). 7 from both sides.

We will look at both.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. Math: Absolute Value The absolute value bars act like a grouping symbol. Since this isn’t possible that means there is no solution to this equation. It's this complex equation. It is. You have these If there is a negative outside the absolute value bar, it stays there. So let's try to do that. So now let's just solve for x. So, there are two solutions to this equation. We're asked to solve for x. So, as we’ve seen in the previous set of examples we need to be a little careful if there are variables on both sides of the equal sign. In fact, we can guarantee that, We do need to be careful however to not misuse either of these definitions. At this point we’ve got two linear equations that are easy to solve. Embedded content, if any, are copyrights of their respective owners. x plus 7's cancel out, and that was intentional. Knowing that the contents within the absolute value symbol should equal 4, it follows that: 3 x + 9 = 6 and 3 x +9 = − 6 ∴ x = − 1, − 5 There is also the fact however that the right number is negative and we will never get a negative value out of an absolute value!

absolute value expression, you could then-- it then turns Now, if we think of this from a geometric point of view this means that whatever \(p\) is it must have a distance of 4 from the origin.

To solve these, we’ve got to use the formula above since in all cases the number on the right side of the equal sign is positive. it looks kind of daunting.

problem solver below to practice various math topics. Before solving however, we should first have a brief discussion of just what absolute value is. think about this is if you could solve for the you take its absolute value, it would be positive 1/7.



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