Solve each equation. 0.08x+0.06(x+12) = 7.72

Question

Accepted Answer

Welcome back. I am so glad you're here. We are given this linear equation 0. X plus 0.24 times parentheses two X plus 11 And parentheses and that's equal to 9.64. Were asked to solve this linear equations that we're solving for X. Well what's the first step in solving a linear equation? We're trying to get X by itself. Well we want to go through the order of operations that we recall from previous lessons, parentheses, exponents, multiplication and division and then addition and subtraction. So starting with parentheses we look and we see parentheses here. But inside those parentheses they're not like terms. We can't combine them. So the first step here is not going to be parentheses or exponents. It's going to be the multiplication and division because squished up in front of these parentheses is this 0.24? And that's telling us to multiply 0.24 by the two terms inside of the parentheses. So that's step one. Let's bring down 0.22 X. Because we can't do anything with that yet. Now let's distribute the 0.24. We're going to multiply so taking 0.24 times two x. That equals a positive 0.48 x. Now distributing the 0.24 times the positive 11 that equals a 2.64. When we multiply 0.24 times 11 and then we can bring down the equals and the 9.64. Okay, there's no more multiplication or division left that we can do here for the time being next. We need to add and subtract. So we're looking for like terms that can be added and subtracted. So we can combine this 0.22 X. And this 0.48 X. When we bring those together we add those up and that equals a 0.7 X. We can bring down the plus 2.64 equals 9.64. Now we're still trying to get that X by itself and we want to bring that 2.64 over to the right hand side of the equation. It's positive, it's being added. So to bring that over we need to subtract it and what we do to one side we need to do to the other. So we'll subtract 2.64 from both sides of the equation on the left. 2.64 -2.640. So all we have left over there is that 0.7 x On the right? 9.64 -2.64 equals a positive seven. Okay, access almost by itself in order to get that 0. over to the other side. We need to do the opposite operation of what's happening to it. So the 0.7 is being multiplied by the X. We need to divide by 0.7 to get that away from the X. Because 0.7 divided by 0.7 That equals one that's like a one X. But what we do to one side, we do to the other. So we're dividing both sides by 0.7. So on the left again that's one X. Or just X. On the right hand side taking seven divided by 0.7. That equals 10. So we have solved for x and it equals 10. We look at our answer choices and this matches with answer choice. A well done. We'll catch you on the next one.

Solve each equation. 0.08x+0.06(x+12) = 7.72

Key Concepts

Distributive Property

Combining Like Terms

Solving Linear Equations

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