Question 37·Easy·Linear Equations in One Variable

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$2x + 8 = 20$

Which equation has the same solution as the given equation?

A question asking for an equation with the same solution is about equivalent equations: the same value of $x$ must make both equations true. A Desmos regression can find that value in the given equation. To make a matching equation by hand, undo an added number by subtracting it from both sides, not just one.

Hints

Hint 1
In a Desmos regression, change $x$ to $x_1$ and $=$ to $\sim$ . Desmos will find the value that balances both sides. What does it show under PARAMETERS?
Hint 2
The target is an equation, not the value of $x$ . To remove the $+8$ while keeping the same solution, subtract $8$ from both sides. What will $2x$ equal?

Step-by-step

Find the solution, then keep it unchanged
Step 1
Find what solves the given equation
Type $2x_1+8\sim20$ in Desmos. The $x_1$ tells Desmos to find a number rather than graph $x$ , and $\sim$ tells it to match the two sides. Under PARAMETERS, it gives $x_1=6$ . So $6$ solves the given equation, but the question asks for an equation, not a number.
Step 2
Remove the added 8 from both sides
An equivalent equation keeps the same solution. Subtract the same amount from both sides to keep the solution unchanged. Subtract $8$ from both sides:
$\begin{aligned}2x+8-8&=20-8\\[1.4em]2x&=12.\end{aligned}$
So $2x=12$ has the same solution as the given equation. Choice B.

Question 37·Easy·Linear Equations in One Variable

Strategy

Hints

Step-by-step

Lessons that teach this

Study Hints

Strategy

Hints

Step-by-step

Lessons that teach this