An equivalent equation has exactly the same solutions as the original. For choices that are equations in one variable, a Desmos regression can find the original solution; then you can test a choice at that value. Here, each equation is linear and has one solution, so a matching value settles it. Changing only one side of an equation changes its solution.
Hints
- Hint 1
An equivalent equation must have the same solution as the original. First find the value of that makes the given equation true, rather than judging the choices by how similar they look.
- Hint 2
A regression can find that value in Desmos. Rename the unknown as and use instead of . Once Desmos reports , which choice has equal sides at that value?
Step-by-step
Approach 1: Find the solution and test a choice
Step 1Find the original equation's solution
Desmos uses for its graph's vertical coordinate, so rename the unknown as and type . The tells Desmos to use a regression to make the sides equal. Under PARAMETERS, it shows , so the original equation's solution is .
- Step 2
Check for the same solution
Every term in the given equation is divisible by , so is a promising choice to test. Put into it:
The sides match. This equation and the original each have one solution, and it's the same value, so they are equivalent. The matching equation is . Choice B.
Approach 2: Divide both sides by 5
Step 1Keep the equation balanced
You can also change the original equation directly. Divide every term on both sides by ; dividing both sides by the same nonzero number keeps the solutions unchanged:
- Step 2
Simplify the divisions
Reduce the three fractions:
Because the division preserved the solutions, this is the equivalent equation. Choice B.