Question

determine which of the following equations is/are true

#1: 3 x 20 = 4(6 + 9)
#2: 4 x 12 = 6 x (8 x 2) 12 + 6 x √64 = 2 x 4 x 8
#3: 4 x 18 - 4 x 6 = 4^2 + 4 x 8

Answer 1

Let's evaluate each equation step by step.

### Equation #1: \(3 \times 20 = 4(6 + 9)\)

1. Calculate the left side:
\[
3 \times 20 = 60
\]

2. Calculate the right side:
\[
6 + 9 = 15
\]
\[
4 \times 15 = 60
\]

Since both sides are equal:
\[
60 = 60
\]
**Equation #1 is true.**

### Equation #2: \(4 \times 12 = 6 \times (8 \times 2) + 6 \times \sqrt{64} = 2 \times 4 \times 8\)

First, evaluate the left side:
1. Calculate the left side:
\[
4 \times 12 = 48
\]

Now evaluate the right side:
1. Calculate \(6 \times (8 \times 2)\):
\[
8 \times 2 = 16
\]
\[
6 \times 16 = 96
\]

2. Calculate \(6 \times \sqrt{64}\):
\[
\sqrt{64} = 8
\]
\[
6 \times 8 = 48
\]

3. Now add those results together:
\[
96 + 48 = 144
\]

Now evaluate the last part of the equation:
1. Calculate \(2 \times 4 \times 8\):
\[
2 \times 4 = 8
\]
\[
8 \times 8 = 64
\]

Now we compile the right side:
\[
96 + 48 \neq 64
\]
Since \(48 \neq 144\):
**Equation #2 is false.**

### Equation #3: \(4 \times 18 - 4 \times 6 = 4^2 + 4 \times 8\)

1. Calculate the left side:
\[
4 \times 18 = 72
\]
\[
4 \times 6 = 24
\]
\[
72 - 24 = 48
\]

2. Calculate the right side:
\[
4^2 = 16
\]
\[
4 \times 8 = 32
\]
\[
16 + 32 = 48
\]

Since both sides are equal:
\[
48 = 48
\]
**Equation #3 is true.**

### Summary:
- **Equation #1 is true.**
- **Equation #2 is false.**
- **Equation #3 is true.**