Solve each equation. 0.5x+ 4/3x= x+10

Question

Accepted Answer

Welcome back. I am so glad you're here. We are given this linear equation we have 0.2 X plus nine X over five which is all equal to five X plus nine. And we are asked to solve this linear equation to solve for X. Well okay well this is yucky. We have this decimal here. We have this fraction here, yuck. Okay let's start off. We see we've got an equal sign so we can get rid of the fraction. We can do that by multiplying every term here by the common denominator. The only denominator here is five so we can multiply everything by five that will get rid of our fraction. So let's start off taking five times 0.2 X five times 0. X equals one X. Or just X awesome. Now taking nine x over five times five while the fives will cancel out and that will just give us a plus nine X. Wonderful. On the right hand side, five X times five that equals 25 X. Thank you. And nine times five is plus 45. Look at that. Goodbye fraction. Goodbye decimal. Wonderful. Now the next step will take here is on the left hand side we've got a couple of like terms we have a one X plus a nine X. One X plus nine X equals 10 X. So we have 10 X equals still 25 X plus 45. Now we want to get all the excess on the same side. So let's bring the 25 X. On the right to the left hand side where the 10 X. Is that 25 X on the right is positive. So we bring it over by subtracting it from both sides of the equation. On the left hand side, 10 X. Is minus 25 X. Is leaves us with negative 15 X. Is on the right hand side. 25 X minus 25 X. That's zero for the excess, that's what we wanted. And then we still have that plus 45 that positive 45 over there. The X. Is almost by itself. It's just being multiplied by that negative 15. How do we get rid of that? Negative 15? We are going to divide because it's being multiplied by the X. We need to divide it by negative 15 and negative 15 divided by negative 15 that equals one. So we've got a one X over there, that's what we want. But what we do to one side we need to do to the other side as well. So we need to divide the 45 by negative 15 as well. As we said we have X by itself on the left hand side on the right hand side, 45 divided by negative 15 that equals negative three. And we have solved for X. X equals negative three. We look at our answer choices. And this matches with answer choice B. Well done. We'll catch you on the next one

Solve each equation. 0.5x+ 4/3x= x+10

Key Concepts

Combining Like Terms

Isolating the Variable

Balancing Equations

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