Absolute Value Equation Calculator
What do you want to calculate.
- Solve for Variable
- Practice Mode
- Step-By-Step
Example (Click to try)
About absolute value equations.
- Get the absolve value expression by itself.
- Set up two equations and solve them separately.
Absolute Value Equation Video Lesson
- Khan Academy Video: Absolute Value Equations
Need more problem types? Try MathPapa Algebra Calculator
Clear Absolute Value Equation Calculator »
Forgot password? New user? Sign up
Existing user? Log in
Absolute Value Equations
Already have an account? Log in here.
- Pranshu Gaba
- Alan Enrique Ontiveros Salazar
- Kai Hsien Boo
- Agnishom Chattopadhyay
- Aditya Virani
- Prince Loomba
- Keshav Ramesh
Absolute value equations are equations involving expressions with the absolute value functions . This wiki intends to demonstrate and discuss problem solving techniques that let us solve such equations.
A very basic example would be as follows:
Find all values of \(x\) satisfying \(|x-2| + |x-4| = 4.\)
Usually, the basic approach is to analyze the behavior of the function before and after the point where they reach 0. For example, for \(|x-a|\) one could analyze the cases where \(x > a\) or \(x < a\), or even \(x = a\) 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. In this wiki, we intend to discuss this techniques along with strategies on when to use which.
Solver Title
Generating PDF...
- Pre Algebra Order of Operations Factors & Primes Fractions Long Arithmetic Decimals Exponents & Radicals Ratios & Proportions Percent Modulo Number Line Mean, Median & Mode
- Algebra Equations Inequalities System of Equations System of Inequalities Basic Operations Algebraic Properties Partial Fractions Polynomials Rational Expressions Sequences Power Sums Interval Notation Pi (Product) Notation Induction Logical Sets Word Problems
- Pre Calculus Equations Inequalities Scientific Calculator Scientific Notation Arithmetics Complex Numbers Polar/Cartesian Simultaneous Equations System of Inequalities Polynomials Rationales Functions Arithmetic & Comp. Coordinate Geometry Plane Geometry Solid Geometry Conic Sections Trigonometry
- Calculus Derivatives Derivative Applications Limits Integrals Integral Applications Integral Approximation Series ODE Multivariable Calculus Laplace Transform Taylor/Maclaurin Series Fourier Series Fourier Transform
- Functions Line Equations Functions Arithmetic & Comp. Conic Sections Transformation
- Linear Algebra Matrices Vectors
- Trigonometry Identities Proving Identities Trig Equations Trig Inequalities Evaluate Functions Simplify
- Statistics Mean Geometric Mean Quadratic Mean Average Median Mode Order Minimum Maximum Probability Mid-Range Range Standard Deviation Variance Lower Quartile Upper Quartile Interquartile Range Midhinge Standard Normal Distribution
- Physics Mechanics
- Chemistry Chemical Reactions Chemical Properties
- Finance Simple Interest Compound Interest Present Value Future Value
- Economics Point of Diminishing Return
- Conversions Roman Numerals Radical to Exponent Exponent to Radical To Fraction To Decimal To Mixed Number To Improper Fraction Radians to Degrees Degrees to Radians Hexadecimal Scientific Notation Distance Weight Time Volume
- Pre Algebra
- One-Step Addition
- One-Step Subtraction
- One-Step Multiplication
- One-Step Division
- One-Step Decimals
- Two-Step Integers
- Two-Step Add/Subtract
- Two-Step Multiply/Divide
- Two-Step Fractions
- Two-Step Decimals
- Multi-Step Integers
- Multi-Step with Parentheses
- Multi-Step Rational
- Multi-Step Fractions
- Multi-Step Decimals
- Solve by Factoring
- Completing the Square
- Quadratic Formula
- Biquadratic
- Logarithmic
- Exponential
- Rational Roots
- Floor/Ceiling
- Equation Given Roots
- Newton Raphson
- Substitution
- Elimination
- Cramer's Rule
- Gaussian Elimination
- System of Inequalities
- Perfect Squares
- Difference of Squares
- Difference of Cubes
- Sum of Cubes
- Polynomials
- Distributive Property
- FOIL method
- Perfect Cubes
- Binomial Expansion
- Negative Rule
- Product Rule
- Quotient Rule
- Expand Power Rule
- Fraction Exponent
- Exponent Rules
- Exponential Form
- Logarithmic Form
- Absolute Value
- Rational Number
- Powers of i
- Partial Fractions
- Is Polynomial
- Leading Coefficient
- Leading Term
- Standard Form
- Complete the Square
- Synthetic Division
- Linear Factors
- Rationalize Denominator
- Rationalize Numerator
- Identify Type
- Convergence
- Interval Notation
- Pi (Product) Notation
- Boolean Algebra
- Truth Table
- Mutual Exclusive
- Cardinality
- Caretesian Product
- Age Problems
- Distance Problems
- Cost Problems
- Investment Problems
- Number Problems
- Percent Problems
- Addition/Subtraction
- Multiplication/Division
- Dice Problems
- Coin Problems
- Card Problems
- Pre Calculus
- Linear Algebra
- Trigonometry
- Conversions
Most Used Actions
Number line.
- \left|3x+1\right|=4
- \left|a-6\right|=\left|6-a\right|
- 1.5\left|3p\right|=4.5
- 4\left|2x-8\right|=9
- \left|3x+4\right|=-3
- 5-\left|2(x+3)\right|=0
absolute-equation-calculator
- High School Math Solutions – Absolute Value Equation Calculator Solving absolute value equations is somewhat tricky; it requires understanding of the absolute value property....
Please add a message.
Message received. Thanks for the feedback.
IMAGES
VIDEO
COMMENTS
For a complete list of Timely Math Tutor videos by course: www.timelymathtutor.com
About absolute value equations. Solve an absolute value equation using the following steps: Get the absolve value expression by itself. Set up two equations and solve them separately.
Solving Absolute Value Equations. 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 original absolute value equation into two parts: positive and negative (±) components.Below is the general approach on how to break them down into two equations:
You get x is equal to 15. To solve this one, add 5 to both sides of this equation. x is equal to negative 5. So our solution, there's two x's that satisfy this equation. x could be 15. 15 minus 5 is 10, take the absolute value, you're going to get 10, or x could be negative 5. Negative 5 minus 5 is negative 10.
This page titled 1.2: Solving Absolute Value Equations is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.
For problems 1 - 5 solve each of the equation. For problems 6 & 7 find all the real valued solutions to the equation. Here is a set of practice problems to accompany the Absolute Value Equations section of the Solving Equations and Inequalities chapter of the notes for Paul Dawkins Algebra course at Lamar University.
To solve absolute value problems with one solution, identify expression in absolute value bars. Recall absolute value is zero only if expression is zero. Make expression equal right-hand side. Use algebra to find x values that satisfy equation. Check solutions by plugging in. Graph solutions on number line. Mark points.
Lesson 2: Solving absolute value equations. Intro to absolute value equations and graphs. Worked example: absolute value equation with two solutions. Worked example: absolute value equations with one solution. ... Report a problem. Stuck? Review related articles/videos or use a hint.
Break the absolute value equation into two equations with positive and negative cases then solve. Therefore, the solution set is [latex]\{ - 3,-1\}[/latex]. Problem 5: Solve the absolute value equation below.
Absolute value equations are equations involving expressions with the absolute value functions. This wiki intends to demonstrate and discuss problem solving techniques that let us solve such equations. A very basic example would be as follows: Find all values of x x satisfying |x-2| + |x-4| = 4. ∣x−2∣ +∣x− 4∣ = 4.
Free absolute value equation calculator - solve absolute value equations with all the steps. Type in any equation to get the solution, steps and graph
The General Steps to solve an absolute value equation are: Rewrite the absolute value equation as two separate equations, one positive and the other negative. Solve each equation separately. After solving, substitute your answers back into original equation to verify that you solutions are valid. Write out the final solution or graph it as needed.
1. Isolate the absolute value expression to one side of the equal sign. 2. Set the inside of the absolute value equal to + and to - the value on the other side of the equal sign (remove the absolute value bars in this step). 3. If needed, solve for the variable in these 2 new equations. 4.
1.6 Practice - Absolute Value Equations Solve each equation. 1) |x|=8 3) |b|=1 5) |5+8a|=53 7) |3k+8|=2 9) |9+7x|=30 11) |8+6m|=50 13) |6−2x|=24 15) −7|−3−3r|=−21 17) 7|−7x−3|=21 19) |−4b−10| 8 =3 ... 1.6 Answers to Absolute Value Equations 1) 8, −8 2) 7,−7 3) 1,−1
This topic covers: - Solving absolute value equations - Graphing absolute value functions - Solving absolute value inequalities. ... Absolute value inequalities word problem (Opens a modal) Our mission is to provide a free, world-class education to anyone, anywhere.
Step 2: Set the argument of the absolute value equal to ± p. Here the argument is 5x − 1 and p = 6. 5x − 1 = − 6 or 5x − 1 = 6. Step 3: Solve each of the resulting linear equations. 5x − 1 = − 6 or 5x − 1 = 6 5x = − 5 5x = 7 x = − 1 x = 7 5. Step 4: Verify the solutions in the original equation. Check x = − 1.
The absolute value is isolated. Since 0 0 is the only number whose absolute value is 0 0, the expression 1 3x − 6 1 3 x − 6 must be equal to 0 0. So, 1 3x − 6 = 0 1 3x − 6 x = 18 Add 6 to both sides of the equation Multiply both sides by 3 1 3 x − 6 = 0 1 3 x − 6 Add 6 to both sides of the equation x = 18 Multiply both sides by 3 ...
How to Solve Tough Absolute Value Equations. In our previous encounter of solving absolute value equations, we dealt with the easy case because the problems involved can be solved in a very straightforward manner.. In tough absolute value equations, I hope you notice that there are two absolute value expressions with different arguments on one side of the equation and a constant on the other side.
38 Chapter 1 Solving Linear Equations SELF-ASSESSMENT 1 I do not understand. 2 I can do it with help. 3 I can do it on my own. 4 I can teach someone else. EXAMPLE 1 Solving Absolute Value Equations Solve each equation. Graph the solutions, if possible. a. ∣ x − 4 ∣ = 6 b. ∣ 3x + 1 ∣ = −5 SOLUTION a. Write the two related linear equations for ∣ x − 4 ∣ = 6.
2) The absolute values (besides being the distance from zero) act as grouping symbols. Once you get to the point that you can actually drop the absolute values, if there is a number in front, that number must be distributed. Example: 14 |x+7| = 2 becomes 14 (x+7) = 2 and 14 (x+7) = -2.
Solving an Absolute Value Equation. Recall that the absolute value of a real number \(a\), denoted \(|a|\), is defined as the distance between zero (the origin) and the graph of that real number on the number line. For example, \(|−3|=3\) and \(|3|=3\). In addition, the absolute value of a real number can be defined algebraically as a piecewise function.
Steps for Solving Linear Absolute Value Equations : i.e. + = 1. Isolate the absolute value. 2. Identify what the isolated absolute value is set equal to… a. If the absolute value is set equal to zero , remove absolute value symbols & solve the equation to get one solution . b. If the absolute value is set equal to a negative number, there is ...
So plus 19 and 1/2. On the left-hand side, these guys obviously cancel out, that was the whole point, and we are left with the absolute value of h on the left-hand side is less than. And then if we have 19 and 1/2, essentially minus 12, 19 minus 12 is 7, so it's going to be 7 and 1/2. So now we have that the absolute value of h is less than 7 ...