Question

1. you are looking for a new phone. the price you want to pay is $200 with an absolute deviation of at most $50. write and solve an absolute value inequality to find which prices meet this condition.

Explanation:

Step1: Define the variable

Let \( x \) be the price of the phone.

Step2: Write the absolute - value inequality

The absolute deviation of \( x \) from \( 200 \) is at most \( 50 \). The formula for the absolute - value inequality is \( |x - 200|\leq50 \).

Step3: Solve the absolute - value inequality

We know that if \( |a|\leq b\) (\(b\geq0\)), then \( -b\leq a\leq b \).
For \( |x - 200|\leq50 \), we have \( - 50\leq x - 200\leq50 \).
Add \( 200 \) to all parts of the compound inequality:
\( -50+200\leq x-200 + 200\leq50+200 \).
\( 150\leq x\leq250 \).

Answer:

The absolute - value inequality is \( |x - 200|\leq50 \) and the solution is \( 150\leq x\leq250 \), which means the price \( x \) of the phone should be between \( \$150 \) and \( \$250 \) (inclusive).