Math! "Real solutions"? HELP

Test Preparation ACT Preparation
1

<p>I came across this math problem in a real ACT practice test and am really confused.</p>

<p>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</p>

<ul>
<li>box thing is signs for a absolute value
so i thought 'Hey, its a quadratic equation' and just did the problem without much affection for the absolute value signs. thus I got answers such as 1 and -3. This didn't match my answers so I made the absolute value minus...as in -x^2-2x.3=0 but this also didn't work.</li>
</ul>

<p>can someone help me
thanks</p>

2

<p>(x-1)(x+3) is the equation factored ignoring absolute values. So x = 1, -3. No other solutions for the quadratic will make it equal to 0. However, in the equation given x is absolute valued. That means x must be positive. 1 will work, as 1 is already positive. -1 will work now as |-1| = 1. The absolute value of -3 is 3, which doesn’t work. You can never input -3 as |-3| = 3. So only +/- 1 works.</p>

<p>So: F. ±1</p>

3

<p>thanks cjgone!</p>