Absolute value equation example 2 | Linear equations | Algebra I | Khan Academy

TL;DR

Isolate the absolute value expression, solve for two possible values, and verify the solutions.

Transcript

So we're given the following equation, that 5 times the absolute value of x plus 3 minus 3 is equal to 7. It's always a little daunting to see an equation with an absolute value sign. And when you only have one of them, like this, what I like to do is isolate it, and just kind of think it through from that point. So let's try to isolate the absolut... Read More

Key Insights

• 😑 Isolate the absolute value expression by canceling out any constants.
• 🙃 Divide both sides by the coefficient of the absolute value expression to isolate it.
• 😑 Consider the positive and negative possibilities for the absolute value expression.
• ❓ Solve for each possibility and verify the solutions to ensure their validity.
• 0️⃣ Absolute value represents the distance from zero.
• ❓ Absolute value equations can have one or two solutions.
• ❎ Solutions can be positive or negative values.

Questions & Answers

Q: How do you isolate the absolute value expression in the equation?

To isolate the absolute value expression, add/subtract any constants on one side of the equation to cancel them out.

Q: Why do we divide both sides by the coefficient of the absolute value expression?

Dividing both sides by the coefficient of the absolute value expression allows us to isolate it completely and solve for its possibilities.

Q: How do we determine the possibilities for the absolute value expression?

The possibilities for the absolute value expression are the positive and negative values that result in the absolute value of the expression being equal to the given value.

Q: Why do we verify the solutions?

Verifying the solutions ensures that they satisfy the original equation and are valid solutions.

Summary & Key Takeaways

• To solve absolute value equations, isolate the absolute value expression.

• Add/subtract to cancel out any constants on one side of the equation.

• Divide both sides by the coefficient of the absolute value expression to isolate it.

• Consider the possibilities for the absolute value expression, both positive and negative.

• Solve for each possibility and verify the solutions.