Solve each linear equation. See Examples 1–3. 0.2x - 0.5 = 0.1...

Question

Solve each linear equation. See Examples 1–3. 0.2x - 0.5 = 0.1x + 7

Accepted Answer

Welcome back everyone in this problem. We want to find a solution for the equation. 0.7 X minus 0.8 equals 0.4 X plus 19. For our answer choices A is 660 B is 6.6 C is 66 and D is 0.66. Now, what are we trying to do here? We want, we want to find the solution. In other words, we want to solve for X. But when you look at our equation, it looks a little bit complicated with those decimal numbers. So if we can rewrite our equation without those decimal numbers, at least for the X terms, then we should be able to solve a little bit easier. So let's try to turn those decimal numbers into integers and see where we go from there. Now, if we look at our, our smallest numbers, 0.4 X, we can turn it into an integer by multiplying by 10. But if we multiply 0.4 X by 10, we'll have to multiply everything by 10. So multiplying the equation by 10. OK. I'm just gonna get better. Trust me. It's gonna make it much easier to work with. But you probably know that 0.7 X multiplied by 10 is seven, X, 0.8 multiplied by 10. Is it 0.4 X multiplied by 10 is four X and 19 multiplied by 10 is 190. No, we have integers and we can go ahead and solve for X. No. The problem is we need all the X terms on one side and the constants on the other side. So to get the X terms on the left hand side, I'm going to try and get rid of the constant. Since my constant is negative eight to get rid of it, I would add eight and I also have to do it to the right hand side. Likewise, on the right hand side to get rid of the constant, I'd have to subtract forex, which means I'd have to also do it on the left hand side. OK? No, seven X minus four X that equals three X negative eight plus eight. Those that equals zero four, X minus four, X equals zero and 190 plus eight is 198. Now, if three X equals 198 that means X equals 198 divided by three and 198 divided by three equals 66. Therefore, X equals 66. And when we go back to our answer choices, that would be answer choice. C thanks a lot for watching everyone. I hope this video helped.

Solve each linear equation. See Examples 1–3. 0.2x - 0.5 = 0.1x + 7

Key Concepts

Linear Equations

Isolating the Variable

Combining Like Terms

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