https://file.aiquickdraw.com/mathbot/file/1726667907745k7bnqpar.jpg

Let's go through the math problems from the image you've uploaded:

### Question 5:
The equation is:
\[
-x + 6 = 3x - 10
\]
We need to solve for $ x $.

Step 1: Add $ x $ to both sides:
\[
6 = 4x - 10
\]

Step 2: Add 10 to both sides:
\[
16 = 4x
\]

Step 3: Divide both sides by 4:
\[
x = 4
\]

Thus, the correct answer is **E. 4**.

---

### Question 6:
Fred's phone plan costs \$25 per month and includes 100 minutes. After that, each extra minute costs \$0.10. Fred has a budget of \$33. This means he has an extra \$8 beyond the initial \$25.

Step 1: Calculate how many extra minutes Fred can use with the \$8:
\[
8 \div 0.10 = 80 \text{ extra minutes}
\]

Step 2: Add the 100 included minutes to the 80 extra minutes:
\[
100 + 80 = 180 \text{ minutes}
\]

Thus, the correct answer is **C. 180**.

---

### Question 7:
The formula for converting Celsius to Fahrenheit is:
\[
f(c) = \frac{9}{5}c + 32
\]
We need to find the Fahrenheit temperature corresponding to 13.0°C.

Step 1: Plug in $ c = 13 $ into the formula:
\[
f(13) = \frac{9}{5}(13) + 32 = 23.4 + 32 = 55.4
\]

Thus, the correct answer is **D. 55.4°F**.

---

Let me know if you need any more explanations!

### 5 Related Questions:
1. How do you solve a two-step linear equation?
2. What other types of fees might Fred need to consider with his phone plan?
3. Can you derive the Celsius to Fahrenheit formula from the Fahrenheit to Celsius formula?
4. How would the solution to the first equation change if the constants were different?
5. What strategies can be used to verify that the budget in Question 6 is not exceeded?

#### Tip:
Always double-check your final answer by substituting it back into the original equation to ensure it works!

What value of x makes the equation -x + 6 = 3x - 10 true?

Learn how to solve the linear equation -x + 6 = 3x - 10 with a clear, step-by-step guide. This problem demonstrates core algebra concepts suitable for students in Grades 8-10.

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