Solve each equation. 0.2x - 0.5 = 0.1x+7

Question

Accepted Answer

Welcome back. I am so glad you're here. We are given this linear equation 0.7 X minus 0.8 and that's equal to 0.5 X plus nine. We are asked to solve this linear equation to solve for X. So we want to get X by itself on one side of the equal sign. So let's bring all of the excess together to the left hand side. This 0.5 X on the right hand side is positive. So to bring it over we're going to subtract doing the opposite operation. Subtract it from both sides. Because what we do to one side we need to do to the other side. So on the left we have 0.7 X minus 0.5 X. That will leave us with 0.2 X. We can bring down this minus 0.8 and that equals on the right hand side, 0.5 X minus 0.5 X is zero excess. Which is just what we had intended. Leaving just this positive nine over there. Now to continue to get X by itself, we want to get this negative 0.8 over to the right hand side where there are no exes. So because that is being subtracted, we do the opposite operation. We are going to add 0.8 and what we do to one side, we do to the other side as well. So on the left we can bring down our 0.2 x negative 0.8 plus 0.8 is the zero that we intended. So that that's gone now that equals nine plus 0.8. That equals 9.8. Alright. Access almost by itself. It just has that 0.2 being multiplied by it. And so we need to again do the opposite operation. So the opposite of multiplication is division. We are going to divide both sides by 0.2. On the left. 0.2 divided by 0.2 is one. So we've got one x over there or just X. Which is what we want On the right hand side. 9.8 divided by 0.2 equals a positive 49. And we have solved for x. x equals 49. We look at our answer choices and that matches with answer choice. A well done. We'll catch you on the next one.

Solve each equation. 0.2x - 0.5 = 0.1x+7

Key Concepts

Solving Linear Equations

Combining Like Terms

Working with Decimals in Equations

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