To solve the given problem, let's carefully examine and solve each part step by step.
### Part 1: Verify the Equation
First, we need to verify the equality of the given equation:
[tex]\[
(2 \times 4) \times 5 = 2 \times (14 \times 10)
\][/tex]
1. Start with the left side of the equation:
[tex]\[
(2 \times 4) \times 5
\][/tex]
- Compute [tex]\(2 \times 4\)[/tex]:
[tex]\[
2 \times 4 = 8
\][/tex]
- Then multiply the result by 5:
[tex]\[
8 \times 5 = 40
\][/tex]
- So, the left side equals 40.
2. Now solve the right side of the equation:
[tex]\[
2 \times (14 \times 10)
\][/tex]
- Compute [tex]\(14 \times 10\)[/tex]:
[tex]\[
14 \times 10 = 140
\][/tex]
- Then multiply the result by 2:
[tex]\[
2 \times 140 = 280
\][/tex]
- So, the right side equals 280.
3. Compare the two results:
[tex]\[
40 \neq 280
\][/tex]
- The equation is not equal. Therefore, the equality does not hold.
### Part 2: Solve for the Missing Value
Now, let's find the missing value in the second equation:
[tex]\[
7 \times \square = \square \times 16
\][/tex]
Let’s denote the missing value by [tex]\( x \)[/tex]. Then the equation becomes:
[tex]\[
7 \times x = x \times 16
\][/tex]
To find [tex]\( x \)[/tex], we need to solve this equation algebraically.
1. Start by writing the equation:
[tex]\[
7x = 16x
\][/tex]
2. To isolate [tex]\( x \)[/tex], we move all [tex]\( x \)[/tex] terms to one side of the equation:
[tex]\[
7x - 16x = 0
\][/tex]
[tex]\[
-9x = 0
\][/tex]
3. Divide both sides by [tex]\(-9\)[/tex]:
[tex]\[
x = 0
\][/tex]
Through algebraic manipulation, we find that [tex]\( x = 0 \)[/tex] is the solution that satisfies the equation.
### Conclusion
- The left side of the initial equation [tex]\((2 \times 4) \times 5\)[/tex] equals 40.
- The right side of the initial equation [tex]\(2 \times (14 \times 10)\)[/tex] equals 280.
- The equality [tex]\((2 \times 4) \times 5 = 2 \times (14 \times 10)\)[/tex] is not true because 40 is not equal to 280.
- For the equation [tex]\(7 \times \square = \square \times 16\)[/tex], the missing value that satisfies this equation is [tex]\( 0 \)[/tex].
