How To Solve Absolute Value Equations, Basic Introduction, Algebra

TL;DR

Absolute value produces a positive result. To solve absolute value equations, create two equations and solve for the variable based on different values for the absolute value expression.

Transcript

what is the absolute value of five and what is the absolute value of negative eight the absolute value of five is five the absolute value of negative eight is positive eight the absolute value cannot produce a negative result it will always produce a positive result or if you have 0 it will give you 0. now let's say if you have an equation for exam... Read More

Key Insights

• 🤘 The absolute value of a number is always positive, regardless of its sign.
• 😑 To solve absolute value equations, create two equations with the absolute value expression equal to positive and negative values, and solve for the variable in both cases.
• ❓ Absolute value equations can have multiple solutions if different values satisfy the equation.

Questions & Answers

Q: What is the absolute value of 5 and -8?

The absolute value of 5 is 5, while the absolute value of -8 is 8. The absolute value always yields a positive result.

Q: How can we solve an equation involving absolute value?

When solving an equation like |x + 2| = 9, create two equations: one with the inside expression equal to 9, and the other with the inside expression equal to -9. Solve both equations separately to find possible values for x.

Q: Can absolute value equations have multiple solutions?

Yes, absolute value equations can have multiple solutions. For example, in the equation |x| = 7, x can be either 7 or -7, as both values satisfy the equation.

Q: What happens if an absolute value equation equals a negative number, like |x| = -2?

An absolute value equation can never equal a negative number. In such cases, there is no solution for the equation. The absolute value only yields zero or positive values.

Summary & Key Takeaways

• Absolute value of a number is always positive.

• To solve an absolute value equation, generate two equations with the absolute value expression equal to a positive and negative value, then solve for the variable.

• Not all absolute value equations have solutions.