If this,than that

Question

1. Equation  is a true equation for a particular value of . Explain why  is also true for the same value of .

1. To solve the equation , Lin divides each side by , and Elena subtracts  from each side.

a. Will both moves lead to the solution? Explain your reasoning.

b. What is the solution?

Answer 1

1. We want to solve for x in the equation 4(x-2)=100.

Distribute the 4: 4x-8=100.

Add 8 to both sides: 4x = 108

Divide by 4 to get x = 27.

Now, plug x=27 in to the second equation: 2(27-2)=50. Subtract: 2(25) = 50. This is true! That's why it works. Two twenty fives make 50.

2. 7.5d = 2.5d

a. Dividing both sides by 2.5 d gives the equation 3=1. This cannot be true! Because we don't know what d is, it could be zero, and dividing by zero is always bad! There's no way to put a quantity into zero parts!

Dividing an unknown out of an equation often results in this type of nonsense answer.

Subtracting the same quantity from both sides is perfectly fine and does lead to the answer:

b. 7.5d -2.5d = 2.5d - 2.5d

5d=0

Divide both sides by 5 to get d=0.

I hope that helps! Let me know if you have any questions, and have fun!

Liz Z.