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

Determine the solution set of 2𝑥 + 5 = −11 using the substitution set {−16, 8, −8, 1}.

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Video Transcript

Determine the solution set of two 𝑥 plus five equals negative 11 using the substitution set negative 16, eight, negative eight, and one.

To solve the equation two 𝑥 plus five equals negative 11, we could have used the balancing method and subtracted five from both sides of the equation then divided by two, and we would have got an answer of 𝑥 equals a number.

However, in this case, we’re asked to use the substitution set. This means that we need to substitute negative 16, eight, negative eight, and one into our equation. Substituting in negative 16 gives us two multiplied by negative 16 plus five.

Two multiplied by negative 16 is negative 32. And negative 32 plus five is equal to negative 27. As this is not equal to negative 11, then the solution set cannot contain negative 16.

When we substitute eight into the equation, we get two multiplied by eight add five. Two multiplied by eight is 16. And 16 plus five is 21. Once again, 21 is not equal to negative 11. Therefore, eight is not in the solution set.

Our third value was negative eight. When we substitute this in, we get two multiplied by negative eight plus five. Two multiplied by negative eight is negative 16. So we are left with negative 16 plus five. Well this does give us an answer of negative 11. Therefore, 𝑥 equals negative eight is in the solution set.

Finally, substituting in 𝑥 equals one gives us two multiplied by one plus five. Two multiplied by one is two. And two plus five equals seven. Therefore, 𝑥 equals one is not in the solution set.

As the only value that gave us an answer of negative 11 was negative eight, our solution set contains the value negative eight i.e., the solution set of two 𝑥 plus five equals negative 11 is negative eight.

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