If the |x + 1| = 6, what are the possible values for x? A.) -5 and 7 B.) -1 and 1 C.) 5 and -7 D.) 5 and -5 E.) 5 and 7 For a more basic example: If |x| = 3, then x could equal 3 or -3, because the absolute value of 3 is 3, and the absolute value of -3 is also 3 |x + 1| = 6x + 1 = 6 or x + 1 = -6 {set the value of the expression inside the absolute value symbols equal to 6 and -6} x = 5 or x = -7 {subtracted 1 from each side in both equations} C.) 5 and -7 are the possible values for xAlso if you take the original equation, |x + 1| = 6, and subtract 6 from each side |x + 1| - 6 = 0 {subtracted 6 from each side} then graph the function, f(x) = |x + 1| - 6, you can see that when the value of y {or f(x)} is equal to 0 {also known as the x-intercept} the value of x is, in fact, equal to -7 and 5, meaning the graph crosses the x-axis at -7 and 5 - Algebra House
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