Chris makes 7 dollars per hour plus a weekly bonus of 10 dollars a week, where x is the number of hours worked and y is the total income earned.

Question

options:

What equation represents this scenario? _______

If Chris' paycheck this week is $94, how many hours did he work? ________

Answer 1

To create the equation that represents Chris's income scenario, we can start with the information provided:

• He earns $7 per hour, which can be expressed as \( 7x \) where \( x \) is the number of hours worked.
• He also receives a weekly bonus of $10.

The total income \( y \) can be represented by the equation:

\[ y = 7x + 10 \]

Now, to determine the number of hours \( x \) Chris worked if his paycheck this week is $94, we can set \( y = 94 \) and solve for \( x \):

\[ 94 = 7x + 10 \]

First, subtract 10 from both sides:

\[ 94 - 10 = 7x \] \[ 84 = 7x \]

Next, divide both sides by 7:

\[ x = \frac{84}{7} = 12 \]

So, Chris worked 12 hours this week.

To summarize:

• The equation is: \( y = 7x + 10 \)
• The number of hours worked is: 12 hours.

Answer 2

Find and correct the error.

x over 4 + 6 > 3


x + 6 > 12


x > 6

options:

6 should have been subtracted first before multiplying by 4 - the true answer should be x > -12
6 should have been subtracted first before multiplying by 4 - the true answer should be x > -12

6 should have been added first before multiplying by 4 - the true answer should be x > 36
6 should have been added first before multiplying by 4 - the true answer should be x > 36

6 should have been subtracted first before multiplying by 4 - the true answer should be x > -3/4
6 should have been subtracted first before multiplying by 4 - the true answer should be x > -3/4

With inequalities you always flip the symbol at the end - the true answer should be x < 6

Answer 3

Let's go through the solution step-by-step to identify the error.

1. Start with the original inequality:

   \[ \frac{x}{4} + 6 > 3 \]

2. To isolate \( \frac{x}{4} \), subtract 6 from both sides:

   \[ \frac{x}{4} > 3 - 6 \]

   Simplifying the right side gives:

   \[ \frac{x}{4} > -3 \]

3. Next, to solve for \( x \), multiply both sides by 4 (note that we do NOT flip the inequality sign when multiplying by a positive number):

   \[ x > -3 \times 4 \]

   This simplifies to:

   \[ x > -12 \]

Based on these steps, the correct inequality is indeed:

\[ x > -12 \]

Now, let's look at the provided options to find the correct statement regarding the error:

• 6 should have been subtracted first before multiplying by 4 - the true answer should be x > -12. (correct statement)

• The other options provided are incorrect interpretations of the inequality manipulation.

So, the correct identification of the error is:

6 should have been subtracted first before multiplying by 4 - the true answer should be x > -12.