Question

solve the inequality. graph the solution, if possible.

1. ( |n + 4| < 5 )
2. ( |6x - 5| geq 19 )
3. ( |m + 4| geq 1 )
4. ( 2|2y - 3| + 8 geq \frac{5}{2} )
5. you are looking for a new phone. the price you want to pay is $200 with an absolute de

most $50. write and solve an absolute value inequality to find which prices meet this con

Explanation:

Step1: Define the variable

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

Step2: Write the absolute - value inequality

The absolute deviation from \( 200 \) is at most \( 50 \). So, \( |x - 200|\leq50 \).

Step3: Solve the compound 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 \( 150\leq x\leq250 \). This means the prices of the phone that meet the condition are between \( \$150 \) and \( \$250 \) (inclusive).