Solving Problems With Absolute Value
The absolute value function exists among other contexts as well, including complex numbers.Note that and For complex numbers , the absolute value is defined as , where and are the real and imaginary parts of , respectively.
We will look at an example first to understand: Example-1 Solve for This is a continuation of my solution given earlier. Please refer to that solution first, before reading this solution.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.We must consider numbers both to the right and to the left of zero on the number line.Notice that both 3 and -3 are three units from zero. Example 1 suggests a rule that we can use when solving absolute value equations.Because we are multiplying by a positive number, the inequalities will not change: −2 ≤ x ≤ 6 Done!Equations with a variable or variables within absolute value bars are known as absolute value equations . how far a number is from zero: "6" is 6 away from zero, and "−6" is also 6 away from zero.So the absolute value of 6 is 6, and the absolute value of −6 is also 6 To show we want the absolute value we put "|" marks either side (called "bars"), like these examples: Rewrite it as: −12 ≤ 3x−6 ≤ 12 Add 6: −6 ≤ 3x ≤ 18 Lastly, multiply by (1/3).If you are a member, we ask that you confirm your identity by entering in your email.You will then be sent a link via email to verify your account.