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[tex]\[
\begin{array}{l}
(2 \times 4) \times 5 = 2 \times (10 \times 2) \\
7 \times \square = \square \times \square \\
16
\end{array}
\][/tex]

Sagot :

GinnyAnsweridn
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].
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