Video: SAT Practice Test 1 • Section 3 • Question 1

Find the value of 𝑥 for the equation (3𝑥 − 4)/𝑘 = 10 when 𝑘 = 2.

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Video Transcript

Find the value of 𝑥 for the equation three 𝑥 minus four all divided by 𝑘 is equal to 10 when 𝑘 is equal to two.

In order to find the value of 𝑥, we need to substitute the value of 𝑘 into our equation. So we need to replace 𝑘 with two. So instead of 𝑘, we’ve replaced it with its value of two. And now that we’ve done that, we only have the variable 𝑥 left in our equation. So we can solve for it.

Our first step will be to get rid of the denominator, the two. And we can do so by multiplying both sides of this equation by two. Because on the left the twos will cancel, so we’ll be left with three 𝑥 minus four. And then on the right, 10 times two is 20.

Our next step to isolate 𝑥 would be to get rid of the negative four. And we can do so by adding four to both sides of the equation. So now, we have that three 𝑥 is equal to 24 because on the left-hand side the fours cancel and on the right 20 plus four is equal to 24.

And finally, our last step to isolate 𝑥 to solve for 𝑥. We must divide both sides of the equation by three because three is being multiplied to 𝑥. So to get rid of it, to do the inverse operation, we must divide by three. On the left, the threes cancel and on the right 24 divided by three is equal to eight.

So the value of 𝑥 is eight.

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