Question 3290
You have the equation |3x + 2| + 4 = 9. Before we worry about the stuff in the absolute value, let's reduce the equation by subtracting 4 from either side.<br>
|3x + 2| + 4 - 4 = 9 - 4, which reduces to |3x + 2| = 5.<br>
What numbers can be in the absolute value sign? You should guess 5 and -5, right. That is |5| = 5 and |-5| = 5. This means, 3x + 2 must equal either 5 or -5.<br>
So how do we find the values for x?<br>
3x + 2 = 5 and <br>
3x + 2 = -5.<br>
x = 1 satisfies the first case (3(1) + 2 = 5) and x = {{{-(7/3)}}} satifies the second equation. Therefore, x = 1 and x = {{{-(7/3)}}} satisfies the equation.