Question

write an equation to model the situation. then solve the equation.

1. you work for 4 hours on friday and 3 hours on saturday. you also recieved a $50 bonus. you earn $127. how much did you earn per hour?

graph the inequality.

1. $p \leq -6$
2. $n > -5$

write an inequality for the graph.

1. graph with number line from -7 to 7, open circle at -2, blue line to the left
2. graph with number line from -7 to 6, closed circle at 6, blue line to the right

Explanation:

Problem 37:

Step1: Define variable

Let \( x \) be the earnings per hour (in dollars).

Step2: Total hours worked

Total hours worked on Friday and Saturday: \( 4 + 3 = 7 \) hours. So total earnings from hourly work: \( 7x \).

Step3: Set up equation

Total earnings (hourly + bonus) is $127. So equation: \( 7x + 50 = 127 \).

Step4: Solve for \( x \)

Subtract 50 from both sides: \( 7x = 127 - 50 = 77 \).
Divide by 7: \( x = \frac{77}{7} = 11 \).

To graph \( p \leq -6 \):

• Draw a number line.
• Locate -6. Since the inequality is \( \leq \), use a closed (filled) circle at -6.
• Shade to the left of -6 (towards negative infinity) to represent all numbers less than or equal to -6.

To graph \( n > -5 \):

• Draw a number line.
• Locate -5. Since the inequality is \( > \), use an open (unfilled) circle at -5.
• Shade to the right of -5 (towards positive infinity) to represent all numbers greater than -5.

Answer:

You earn $11 per hour.

Problem 38: