# Write an absolute value equation that has 3 and 11 as its solution

So let's try to do that.

We're just subtracting 7 from both sides. This is the solution for equation 2.

If these two things are equal and we are being told that they are, then if you add something on this side, the only way that the equality will hold is if you still do it on the left-hand side.

It's this complex equation. Writing an Equation with a Known Solution If you have values for x and y for the above example, you can determine which of the two possible relationships between x and y is true, and this tells you whether the expression in the absolute value brackets is positive or negative.

## Write an absolute value equation to satisfy the given solution set

And then we're left with 6 minus 4, which is just 2. So that's how we got this. Let's look at some examples. To solve this, you have to set up two equalities and solve each separately. Plug these values into both equations. So how can we reason through this? So I want to get rid of this positive 4. When you take the absolute value of a number, the result is always positive, even if the number itself is negative.

So you could almost treat this expression-- the absolute value of x plus 7, you can just treat it as a variable, and then once you solve for that, it becomes a simpler absolute value problem. And just think about that for a second.

### How to write an absolute value equation

And so what does this get us? We're just going to solve for the absolute value of x plus 7. Plug in known values to determine which solution is correct, then rewrite the equation without absolute value brackets. So that's going to be 14 absolute values of x plus 7, 14 times the absolute value of x plus 7. If you answered no, then go on to step 3. So this is 8 times the absolute value of x plus 7 plus in that same color-- is equal to negative 6 times the absolute value of x plus 7 plus 6. The negative 6 and the 6 x plus 7's cancel out, or absolute values of x plus 7's cancel out, and that was intentional. You have these absolute values in it. So you could almost treat this expression-- the absolute value of x plus 7, you can just treat it as a variable, and then once you solve for that, it becomes a simpler absolute value problem. Writing an Equation with a Known Solution If you have values for x and y for the above example, you can determine which of the two possible relationships between x and y is true, and this tells you whether the expression in the absolute value brackets is positive or negative. Set Up Two Equations Set up two separate and unrelated equations for x in terms of y, being careful not to treat them as two equations in two variables: 1. This means that any equation that has an absolute value in it has two possible solutions. Follow these steps to solve an absolute value equality which contains one absolute value: Isolate the absolute value on one side of the equation.

So that's going to be equal to 2. Follow these steps to solve an absolute value equality which contains one absolute value: Isolate the absolute value on one side of the equation. Is the number on the other side of the equation negative?

So that's how we got this. Because the original equation contained an absolute value, you're left with two relationships between x and y that are equally true. When you take the absolute value of a number, the result is always positive, even if the number itself is negative.

### An absolute value equation that has 3 and 11 as its solutions

And just think about that for a second. Writing an Equation with a Known Solution If you have values for x and y for the above example, you can determine which of the two possible relationships between x and y is true, and this tells you whether the expression in the absolute value brackets is positive or negative. Let's look at some examples. It's this complex equation. When you take the absolute value of a number, the result is always positive, even if the number itself is negative. We can't, of course, only do that to the right-hand side. This is solution for equation 1. Now the key here-- at first it looks kind of daunting. The second equation will set the quantity inside the bars on the left side equal to the opposite of the quantity inside the bars on the right side. So that's how we got this. The first equation will set the quantity inside the bars equal to the number on the other side of the equal sign; the second equation will set the quantity inside the bars equal to the opposite of the number on the other side. The first equation will set the quantity inside the bars on the left side equal to the quantity inside the bars on the right side. We're just going to solve for the absolute value of x plus 7. If you plot the above two equations on a graph, they will both be straight lines that intersect the origin.

The negative 6 and the 6 x plus 7's cancel out, or absolute values of x plus 7's cancel out, and that was intentional.

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