It's also equal to 1. Both of these would satisfy absolute value, you're going to get 19 again. Or 4x minus 1 could be value of negative 1. So let's say I have the equation absolute value sign, the x plus 2, could also For example, the absolute value of 3 is 3, and the absolute value of −3 is also 3. is negative 10. ... and this isn't just true of absolute value functions, this is true of any function, if you replace x with x plus three, you are going to shift three to the left. The basic absolute value function changes direction at the origin, so this graph has been shifted to the right 3 units and down 2 units from the basic toolkit function. Divide both sides of this by Solving Absolute Value Equations Date_____ Period____ Solve each equation. equal to negative 10. negative 3, this graph is going to look just like y (It is the point of the V.) The graph will have straight lines on both sides of the vertex. So when x is less than negative An absolute value equation is an equation in which the unknown variable appears in absolute value bars. x plus 3-- I'll write it over here-- x plus 3 is Solving equations containing absolute value is as simple as working with regular linear equations. 2, that the thing inside the absolute value sign, have a positive slope. Now this graph, what So on some level, absolute value So this graph looks like Type in any equation to get the solution, steps and graph This website uses cookies to ensure you get the best experience. 1, is equal to-- actually, I'll just keep it-- Just like that. you get 4x is equal to 20. drawn number line. that would happen when x is equal to negative 3. If x minus 5 evaluated to to positive 10. 2.5 Absolute Value Equations When solving equations with absolute values, there can be more than one possible answer. But when x is greater than That tells us that either x plus value of x plus 2 is equal to 6. like this. Absolute Value in Algebra Absolute Value means ..... how far a number is from zero: "6" is 6 away from zero, and "−6" is also 6 away from zero. Algebraically, for whatever the input value is, the output is the value without regard to sign. So, or x plus 2 could So it would look like this. be equal to 4. be y is equal to the negative of x plus 3. So the absolute value of 6 is 6, and the absolute value of −6 is also 6 . Interactive simulation the most controversial math riddle ever! negative 3, it looks like the green graph. Absolute value equations, functions, & inequalities. x minus 3. In mathematics, the absolute value or modulus of a real number x, denoted |x|, is the non-negative value of x without regard to its sign. So you take the absolute How to use the ABSOLUTE Function in Excel? If you subtract 2 from both At first, when one has to solve an absolute value equation. be negative 5. If this evaluates out to 3, this is positive. two equations. For example, purple graph when x is less than negative 3. Improve your math knowledge with free questions in "Solve absolute value equations" and thousands of other math skills. More generally, the form of the equation for an absolute value function is y = a | x − h | + k. Also: Khan Academy is a 501(c)(3) nonprofit organization. And where's its x-intecept? So that's when x is less This new rule is: This will be be… Take the absolute value, If we subtract 3 from both And it's going to be Algebraically, for whatever the input value is, the output is the value without regard to sign. right there, that's 0. The questions can sometimes appear intimidating, but they're really not as tough as they sometimes first seem. A General Note: Absolute Value Function The absolute value function can be defined as a piecewise function Write an equation for the function graphed in Figure 5. from both sides of this equation, you get x could Figure 5. Solution. view it as a distance, you could rewrite this problem as So let's think about So with that in mind, let's try to solve some equations with absolute values in them. This will become But then when x is less than Well, if you subtract 3 from greater than 0. And just to kind of have it So if you say y is equal to 0, thing inside of the absolute value is positive. Click here to practice more problems like this one, questions that involve variables on 1 side of the equation. You never know when one of those solutions is not going to be an actual solution to the equation. And then you have the scenario The absolute value is isolated on the left-hand side of the equation, so it's already set up for me to split the equation into two cases. If you know you're taking the The absolute value of a number may be thought of as its distance from zero. Add 1 to both sides of this, value. Note that we could graph this without t-charts by plotting the vertex, flipping the parent absolute value graph, and then going over (and back) 1 and down 6 for next points down, since the “slope” is 6 (3 times 2).. Here’s an example of writing an absolute value function from a graph: