*The distance from \(x\) to 5 can be represented using the absolute value as \(|x−5|\).*We want the values of \(x\) that satisfy the condition \(| x−5 |\leq4\).

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.

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

Distances in the universe can be measured in all directions.

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.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.Solution Using the variable \(p\) for passing, \(| p−80 |\leq20\) Figure 1.6.4 shows the graph of \(y=2|x–3| 4\).The graph of \(y=|x|\) has been shifted right 3 units, vertically stretched by a factor of 2, and shifted up 4 units.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.To get each piece, you must figure out the domain of each piece.This method is highly beneficial when the question writer asks for the number of solutions instead of the actual solutions.Algebraically, for whatever the input value is, the output is the value without regard to sign.Example \(\Page Index\): Determine a Number within a Prescribed Distance Describe all values \(x\) within or including a distance of 4 from the number 5.

## Comments How To Solve Problems With Absolute Value

## 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.…

## 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.…

## 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.…

## 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 - ChiliMath

Solving absolute value equations is as easy as working with regular linear equations. The only additional key step that you need to remember is to separate 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 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.…

## Absolute Value Equations

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.…