Sure, let's go through each part step by step.
### Question 1.2: Simplify the expression [tex]\((15 + 20) \div 7 - 2\)[/tex]
1. Calculate the sum inside the parentheses:
[tex]\[
15 + 20 = 35
\][/tex]
2. Divide the result by 7:
[tex]\[
35 \div 7 = 5
\][/tex]
3. Subtract 2 from the result:
[tex]\[
5 - 2 = 3
\][/tex]
Therefore, the simplified result of [tex]\((15 + 20) \div 7 - 2\)[/tex] is [tex]\(3\)[/tex].
### Question 2: Integers
#### 2.1 Evaluate the truth of the following statements:
1. [tex]\(-5(2 + 1) = (-5 \times 2) + (-5 \times 1)\)[/tex]
- Simplifying the left-hand side:
[tex]\[
-5 \times (2 + 1) = -5 \times 3 = -15
\][/tex]
- Simplifying the right-hand side:
[tex]\[
(-5 \times 2) + (-5 \times 1) = -10 + (-5) = -15
\][/tex]
- Both sides are equal, so the statement is True.
2. [tex]\( x \times (-1) = (-1) \times x \)[/tex]
- This is a fundamental property of multiplication that states that the order of multiplication does not affect the result. Therefore, the statement is always True.
#### 2.2 Simplify the expression [tex]\((-14 + 5) \times -8\)[/tex]
1. Calculate the sum inside the parentheses:
[tex]\[
-14 + 5 = -9
\][/tex]
2. Multiply the result by -8:
[tex]\[
-9 \times -8 = 72
\][/tex]
Therefore, the simplified result of [tex]\((-14 + 5) \times -8\)[/tex] is [tex]\(72\)[/tex].
To summarize:
1. The simplified result of [tex]\((15 + 20) \div 7 - 2\)[/tex] is [tex]\(3\)[/tex].
2. The statement [tex]\(-5(2 + 1) = (-5 \times 2) + (-5 \times 1)\)[/tex] is True.
3. The statement [tex]\(x \times (-1) = (-1) \times x\)[/tex] is True.
4. The simplified result of [tex]\((-14 + 5) \times -8\)[/tex] is [tex]\(72\)[/tex].
