Final answer:
Upon solving the equation presented, it's clear that the two sides of the equation -20 [3/-5+(-7)/-10] and [-20+3/-5]+(-7)/-10 do not equate to the same value. The left-hand side simplifies to -2, while the right-hand side simplifies to 412.7, proving the original equation incorrect.
Step-by-step explanation:
The student has presented the mathematical equation -20 [3/-5+(-7)/-10] = [-20+3/-5]+(-7)/-10 and is seeking verification of its correctness. To solve, we must simplify each side of the equation following the appropriate order of operations (PEMDAS/BODMAS) which stands for Parentheses/Brackets, Exponents/Orders, Multiplication/Division (from left to right), and Addition/Subtraction (from left to right).
Firstly, simplify the expressions within the brackets:
- 3/-5+(-7)/-10 becomes -3/5 + 7/10 which simplifies further to 1/10.
- [-20+3/-5] becomes -20 -3/5 which can be rewritten as -100/5 -3/5 giving -103/5.
Then multiply by -20:
- For the left-hand side: -20 x 1/10 equals -2.
- For the right-hand side: -20 x [-103/5] equals [-20 x -103/5] plus (-7)/-10, which simplifies to 2060/5 + 7/10 giving 412 + 0.7 or 412.7.
On comparing both sides, it's evident that -2 does not equal 412.7, therefore the original equation is incorrect.