Question Video: Solving Two-Step Equations | Nagwa Question Video: Solving Two-Step Equations | Nagwa

Question Video: Solving Two-Step Equations Mathematics • Sixth Year of Primary School

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Solve (𝑥 + 3)/5 = 10.

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Video Transcript

Solve 𝑥 plus three over five equals 10.

We know that 𝑥 plus three over five equals 10. And to solve for 𝑥, we need to get it by itself. We need to isolate it. And that means we need to undo the operations that are being done to 𝑥. In the numerator, we have some number 𝑥 plus three. And whatever that number plus three is is being divided by five. And that means to find out what that number is, we first need to undo this division.

And we can do that by multiplying by five. But if we multiply by five on the left, we need to multiply by five on the right. On the left, the five in the numerator and the five in the denominator cancel out, leaving us with 𝑥 plus three. And on the right, we have 10 times five, which is 50. And now, we have a simple equation, 𝑥 plus three equals 50. So, we subtract three from both sides. And we get 𝑥 equals 47.

Why couldn’t we subtract three from both sides? What would happen if we did? On the left, we would have 𝑥 plus three over five minus three. And on the right, we would have seven. Now, this is still a true statement. 𝑥 plus three over five minus three does equal seven. However, we’re no closer to solving for 𝑥. And that’s because the entire numerator is being divided by five. And we can’t take this plus three out of the numerator. This is because we have to reverse the operations in the contrary order than when we started.

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