# How To Solve Problems With Absolute Value

Analysis Note that $\begin -4&x-5 & x-5&\leq4 \1&x & x&9 \end$ So $$|x−5|\leq4$$ is equivalent to $$1x\leq9$$.However, mathematicians generally prefer absolute value notation.

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Today, astronomers can detect galaxies that are billions of light years away.

Distances in the universe can be measured in all directions.

In this wiki, we intend to discuss this techniques along with strategies on when to use which.

is not a possible solution, but it does not mean it's not a possible solution for Case 1 because we're simply going piece by piece in this piecewise function--in the end we will take the union of all possible solutions.

Thus, the solutions are Sometimes absolute value equations have a ridiculous number of cases and it would take too long to go through every single case.

Therefore, we can instead graph the absolute value equations using the definition of absolute value as a piecewise function.A very basic example would be as follows: if required.However, these problems are often simplified with a more sophisticated approach like being able to eliminate some of the cases, or graphing the functions.As such, it is useful to consider distance as an absolute value function.In this section, we will investigate absolute value functions.Instead, the width is equal to 1 times the vertical distance as shown in Figure $$\Page Index$$.From this information we can write the equation $\begin f(x)&=2|x-3|-2, \;\;\;\;\;\; \text \ f(x)&=|2(x-3)|-2, \;\;\; \text \end$ Analysis Note that these equations are algebraically equivalent—the stretch for an absolute value function can be written interchangeably as a vertical or horizontal stretch or compression.The best that manufacturers can do is to try to guarantee that the variations will stay within a specified range, often ±1%, ±5%, or ±10%. Use the absolute value function to express the range of possible values of the actual resistance. The absolute value of the difference between the actual and nominal resistance should not exceed the stated variability, so, with the resistance $$R$$ in ohms, $|R−680|\leq34$ Exercise $$\Page Index$$ Students who score within 20 points of 80 will pass a test.Write this as a distance from 80 using absolute value notation.Recall that in its basic form $$f(x)=|x|$$, the absolute value function, is one of our toolkit functions.The absolute value function is commonly thought of as providing the distance the number is from zero on a number line.

## Comments How To Solve Problems With Absolute Value

• ###### Absolute Value Equations Brilliant Math & Science Wiki

Absolute value equations are equations involving expressions with the absolute value functions. This wiki intends to demonstrate and discuss problem solving.…

• ###### Intro to absolute value equations and graphs video Khan.

The absolute value of negative 7,346 is equal to 7,346. So with that in mind, let's try to solve some equations with absolute values in them. So let's say I have the.…

• ###### Solving absolute value equations and inequalities Algebra 1.

You can replace above with ≥ and with ≤. When solving an absolute value inequality it's necessary to first isolate the absolute value expression on one.…

• ###### Solving Absolute Value Equations - Example 1 - YouTube

Thanks to all of you who support me on Patreon. You da real mvps! \$1 per month helps. https//. Solving.…

• ###### Algebra - Absolute Value Equations - Pauls Online Math Notes

We will then proceed to solve equations that involve an absolute value. We will also work an example that involved two absolute values.…

• ###### Algebra - Absolute Value Equations Practice Problems

Here is a set of practice problems to accompany the Absolute Value Equations section of the Solving Equations and Inequalities chapter of the.…

• ###### Solving Equations Containing Absolute Values - SOS Math

Step2 Set the quantity inside the absolute value notation equal to + and - the quantity on the other side of the. Step 3 Solve for the unknown in both equations.…

• ###### Solving Simpler Absolute-Value Equations Purplemath

Demonstrates how to solve absolute-value equations, and explains the reasoning behind the algebra. Provides an example of how graphing can be used to.…