I see that you've uploaded an image with several math questions. I will extract the content and solve them one by one for you. Let me transcribe the problems first:

Question 1:

Solve for $x$.

$7x - 10 = 2$

Question 2:

Evaluate the following: $\frac{3}{4} + \frac{5}{12}$

Question 3:

At a carnival, there are 4 white tents and 7 blue tents. Suppose you randomly select a tent from the carnival. What is the probability that the tent is blue? Express your answer as a fraction in simplest form.

Question 4:

Evaluate the following expression: $7 + 8 \div 2^3$

Question 5:

Mother bought 8 oranges. She gave $\frac{1}{2}$ of them to Sarah and $\frac{1}{4}$ of them to Peter. How many oranges does she have left?

Let’s go ahead and solve these questions.

Solution 1:

Solve for $x$ in the equation $7x - 10 = 2$.

1. Add 10 to both sides: $7x = 12$

2. Divide both sides by 7: $x = \frac{12}{7}$

Thus, $x = \frac{12}{7}$.

Solution 2:

Evaluate $\frac{3}{4} + \frac{5}{12}$.

To add fractions, find a common denominator. The least common denominator (LCD) of 4 and 12 is 12.

$\frac{3}{4} = \frac{9}{12}, \quad \frac{5}{12} = \frac{5}{12}$

Now, add the fractions: $\frac{9}{12} + \frac{5}{12} = \frac{14}{12} = \frac{7}{6}$

Thus, $\frac{3}{4} + \frac{5}{12} = \frac{7}{6}$.

Solution 3:

Find the probability of selecting a blue tent.

There are 4 white tents and 7 blue tents, so the total number of tents is: $4 + 7 = 11$

The probability of selecting a blue tent is the ratio of blue tents to the total number of tents: $\text{Probability} = \frac{7}{11}$

Thus, the probability of selecting a blue tent is $\frac{7}{11}$.

Solution 4:

Evaluate $7 + 8 \div 2^3$.

First, apply the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

1. Calculate the exponent: $2^3 = 8$

2. Perform the division: $8 \div 8 = 1$

3. Add the result to 7: $7 + 1 = 8$

Thus, $7 + 8 \div 2^3 = 8$.

Solution 5:

Determine how many oranges are left after Mother gives some away.

Mother bought 8 oranges. She gave half to Sarah: $\frac{1}{2} \times 8 = 4 \text{ oranges to Sarah}$

She gave a quarter to Peter: $\frac{1}{4} \times 8 = 2 \text{ oranges to Peter}$

The total number of oranges given away is: $4 + 2 = 6$

So, the number of oranges left is: $8 - 6 = 2$

Thus, Mother has 2 oranges left.

Summary of Answers:

1. $x = \frac{12}{7}$
2. $\frac{7}{6}$
3. $\frac{7}{11}$
4. 8
5. 2 oranges left

Would you like further clarification or more details on any of these solutions?

Here are 5 related questions to expand your understanding:

1. How would the solution for $7x - 10 = 5$ differ from Question 1?
2. What happens if you subtract fractions instead of adding, like $\frac{3}{4} - \frac{5}{12}$?
3. If there were 5 blue tents and 4 white tents, how would the probability change?
4. How would the expression in Question 4 change if it was $7 + 8 \div 2^4$?
5. What if Mother bought 10 oranges and gave $\frac{1}{3}$ to Sarah and $\frac{1}{5}$ to Peter?

Tip: When working with fractions, always check if you can simplify them before performing operations to make calculations easier.