Video: Finding the Solution Set of Two-Step Linear Equations from a Given Substitution Set

Find the solution set of 2𝑥 − 4 = 16 using the substitution set {20, 6, 10, 3}.

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Video Transcript

Find the solution set of two 𝑥 minus four equals 16 using the substitution set 20, six, 10, and three.

To find the solution set, we’ll need to take our equation two 𝑥 minus four equals 16 and then substitute each value from the substitution set in for 𝑥. Our substitution set has four values. We’ll need to solve this equation four times and find out which of the values make the statement true.

Two times 20 minus four equals 16. Two times six minus four equals 16. Two times 10 minus four equals 16. And two times three minus four equals 16. We’ll start on the left. Two times 20 equals 40. 40 minus four equals 36. 36 is not equal to 16. And that means 20 is not part of the solution set. Moving onto the next option, two times six equals 12. 12 minus four equals eight. Eight is not equal to 16. And that means six is not part of the solution set.

Two times 10 minus four equals 16. Two times 10 equals 20 minus four equals 16. We have a true statement: 16 does equals 16. And that means 10 can be included in the solution set. Now we need to check our last option. Two times three equals six minus four equals two. Two is not equal to 16. And that means three does not belong in the solution set. For this equation, the solution set only includes 10. It’s the set 10.

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