Understanding Absolute Value Inequalities

What is the first step in solving an absolute value inequality like |1/3 C - 4| ≤ 10?

• Add 4 to both sides of the inequality

• Multiply both sides by 3

• Set up a compound inequality

• Subtract 10 from both sides

When transforming |1/3 C - 4| ≤ 10 into a compound inequality, what should be the range of values?

• -10 ≤ C ≤ 10

• -10 ≤ 1/3 C - 4 ≤ 10

• 0 ≤ 1/3 C - 4 ≤ 10

• -4 ≤ 1/3 C ≤ 4

What is the purpose of adding 4 to all sides of the compound inequality?

• To eliminate the absolute value

• To isolate the variable C

• To simplify the inequality

• To balance the equation

After setting up the compound inequality, what operation is performed to isolate C?

• Subtract 4 from all sides

• Add 10 to all sides

• Multiply all sides by 3

• Divide all sides by 3

What is the final solution for C in the inequality |1/3 C - 4| ≤ 10?

• 0 ≤ C ≤ 10

• -6 ≤ C ≤ 14

• -10 ≤ C ≤ 10

• -18 ≤ C ≤ 42