# How do I solve this absolute value ACT math problem?

 0 What are the real solutions to the equation |x|^2 + 2|x|-? 3 = 0 ? F. ±1 G. ±3 H. 1 and 3 J. ?1 and ?3 K. ±1 and ±3 I tried factoring it and got 1 and -3, but that doesn't match any of the choices. How do I find the correct answer? asked 22 Jan '16, 16:24 Sam_PrepScholar 1.4k●172●174●182

 0 You're right that the equation factors out to (x-1)(x+3) if you ignore the absolute value signs. All you have to do is take one more step and plug the solutions back in. If you put -3 into the original equation, it doesn't end up equalling zero because the absolute value signs turn the -3 into a regular positive 3. 3^2 + 2(3) -3 = 0 9 + 6 - 3 = 0 12 = 0 <------- NOPE! Both 3 and -3 can be ruled out as solutions. Now, we can try plugging in 1. Even with the absolute value signs, 1 works as a solution. 1^2 + 2(1) -3 = 0 1 + 2 - 3 = 0 0 = 0 <------- YEP! This means that -1 also works, because -1 and 1 have the same absolute value. The answer to the question is choice F. answered 22 Jan '16, 16:31 Sam_PrepScholar 1.4k●172●174●182

Related articles

 toggle preview

Markdown Basics

• *italic* or _italic_
• **bold** or __bold__