TenMarks teaches you how to solve two step rational equations.
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Learn About Two Step Rational Equations Let’s learn about two-step equations where we’ve got to apply two different steps to solve it. We’re given two problems. The first one is r+7/4=5. So, step one is we’ve got a variable which is being divided by four. So, the first thing we do is we write r+7/4 and we multiply the left side by four and the right side by four. I took the denominator because we need to remove that. We multiply the left hand side of the equation and the right hand side of the equation by four. What do I get? We get r+7=4/4 is 1, 5x4=20. Now that I have r+7=20, the variable can be separated by subtracting seven from the left and seven from the right, r+7-7 is r, 20-7 is 13 so the answer is r=13. Now, let’s try the second problem which is -1=5b/8+3/8. So, the second problem is -1=5b/8+3/8. Let’s try and solve this. So, what do we see? -1=5b/8+3/8, I’m just going to flip this around to make it easy. 5b/8+3/8=-1, I just moved the right hand side to left and left to right. No change or whatsoever. So, the first thing that I see is the variable part has something being added to it. So, we have to subtract 3/8 from the left and from the right. What am I left with? What I’m left with is 5b+3/8-3/8=5b/8=-1-3/8, I just subtracted this from this. Now, since the right side has got a whole number and a fraction, let’s convert the whole number to fractions. -1 can be multiplied by 8 on top and 8 on the bottom,-3/8. All I’m trying to do is get this to have the same denominator as 3/8. So, -1x8 is -8/8-3/8. I can subtract this, -8, -3 is -11/8 since the denominators were the same. So now, what I have is 5b/8=-11/8. Since 5b/8=-11/8, 5b is being divided by eight so let’s multiply it by eight on the left and multiply it by eight on the right. What am I left with? 5b on the left because 8/8 is 1 and -11 x 8/8 is -11. 8 and 8 cancel out. So 5b=-11, b is being multiplied by five so let’s divide it by five in both sides. You notice what I’m doing is I’m just looking at the variable, the action or the constant next to it and if it’s being multiplied to b, I’m dividing it. So 5b/5 is b, -11/5 is -11/5, so the final answer is b=-11/5.
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