1. Solve each absolute value equation or inequality and choose the correct answer from the choices provided. |x| + 5 = 18 (1 point) 5 or –5 13 or –13 18 or –18 23 or –23 2. |x + 3| < 5 (1 point) –8 < x < 2 –2 < x < 8 3 < x < 5 –3 < x < 5 3. |–3n| – 2 = 4 (1 point) 2 or –2 3 or –3 4 or –4 6 or –6
To solve absolute value equations, you need to follow these steps:
Step 1: Isolate the absolute value expression on one side of the equation.
Step 2: Set up two separate equations - one positive and one negative - by removing the absolute value notation.
Step 3: Solve each equation separately for the variable.
Step 4: Check the solutions in the original equation.
Let's apply these steps to solve the given equations:
1. |x| + 5 = 18:
Subtracting 5 from both sides, the equation becomes:
|x| = 13
Setting up the positive equation:
x = 13
Setting up the negative equation:
x = -13
So the correct answer is 13 or -13.
2. |x + 3| < 5:
Subtracting 3 from both sides, the equation becomes:
|x| < 2
Setting up the positive equation:
x < 2
Setting up the negative equation:
-x < 2
Multiplying both sides by -1 (and reversing the inequality):
x > -2
Considering the overall solution, the correct statement is:
-2 < x < 2
So the correct answer is -2 < x < 2.
3. |–3n| – 2 = 4:
Adding 2 to both sides, the equation becomes:
|–3n| = 6
Setting up the positive equation:
-3n = 6
Dividing both sides by -3:
n = -2
Setting up the negative equation:
-(-3n) = 6
Simplifying:
3n = 6
Dividing both sides by 3:
n = 2
Therefore, the correct answer is 2 or -2.
I hope this helps! Let me know if you have any further questions.
|x| + 5 = 18
|x| = 13
x = ±13
|x+3| < 5
x+3 < 5 if x >= -3
x < 2
so, -3 <= x < 2
or
x+3 > -5 if x < -3
x > -8
so, -8 < x < -3
result: -8 < x < 2
|-3n|-2 = 4
|-3n| = 6
|3n| = 6 since |-3n|=|3n|
3n = ±6
n = ±2