TenMarks teaches you how to write and solve two step equations and their applications.
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Learn about Two Step Equations and Their Applications In this lesson, let's learn how to we solve two-step equations and how do we apply them. We’ll do two problems. The first one wants us to solve 2×x+5=11. The reason this is called a two-step equation is if we see the variable x, first it’s been multiplied by 2, so step one, somebody multiplied x by 2 and then they added 5 to it. They added 5 to it to get 11. In order to solve this, we have to undo both these operations. Since first x was multiplied by 2 and then 5 was added, we have to inverse this first. First, you subtract 5 because 5 was added to it and then we divide by 2. Let me show you how we do this. So, we’ve got 2x+5=11. First, what we do is we subtract 5 from both sides. We get 2x=11-5 is 6 then we divide by 2 which gives me 2x÷2 is x equals 6÷2 is 3, so x=3 is the answer. Let’s see if we substitute the value if this is correct. So, instead of x, if I had 3, that would be 2×3=6=5, that would indeed be 11. So, x=3 is the answer. Let's learn how we apply two-step equations to solve real life problems. So it says, “Chris belongs to the Student Music Club and bought a discount card for $19.95 which allows him to buy each CD for $3.95.” It looks like after a year Chris spent $63.40. We need to write and solve an equation to find how many CDs he bought throughout the year. So what do we know? The discount card was $19.95 and then one CD is $3.95, so he if bought x CDs, that would cost him x×$3.95. So, what do we know? Chris has spent $63.40. What we know is $63.40 equals what he spent on the discount card which is $19.95+x CDs which is x×$3.95. So, what he has spent is $19.00+$0.95+$3.95×x, x being the number of CDs and all of these totals $63.40. So, this is our equation, 19.95+3.95×x=63.40. How do we solve it? This is the variable. First, it’s the multiplied then added. First, we subtract. What do I get? This is 45 and this is 29 is 3, 51 is 4, so 3.95x=43.45 or I have to divide both sides by 3.95, so I get 43.45÷3.95 which is 11. It looks like Chris bought 11 CDs. If this was true, 11 CDs would cost him 11×$3.95 which is $43.45 and then you add to that membership and he gets $63.40. The key thing to remember here is when you're solving two-step equations, we have to figure out this is the first operation multiplied by two, this is the second operation. We always undo the second operation first and then undo the first one.