Steps To Solve For Variables In Equations -How To Solve Equations- How To Solve Multi-Step Equations

In this video we go through and explain the steps to solve for variables in equations. We go through a couple examples showing the steps to solve equations.

Transcript/notes
Steps to solving equations
When we want to solve equations, such as 7r minus 6 equals 3 times the quantity r plus 6 minus 2r, there are 2 basic things we need to do to solve equations. First is change the equation so that all the terms with a variable are on one side of the equation, and second is to get all terms with only numbers on the other side of the equation.

In order to solve equations, there are some steps that can be helpful. And we are going to use this equation to demonstrate each of the steps.

Step 1 is to remove all parenthesis on both sides of the equation by using the distributive property. For instance in our equation, in parenthesis, we have r plus 6. To remove the parenthesis, we can use the distributive property to distribute the 3 to the terms in the parenthesis. And doing that, we have 3 times r, which is 3r, and 3 times 6, which is 18. So, this gives us a new equation of 7r minus 6 equals 3r plus 18 minus 2r.

Step 2 is to combine like terms on both sides of the equation. Like terms are terms with the same variables. In our equation, on the right side, we have the like terms of 3r and -2r, so we can combine them, which gives us 1r, or just r. And now our equation is 7r minus 6 equals r plus 18.
Step 3 is to place all terms with a variable on one side of the equation, and all the terms that do not have a variable on the other side of the equation.

In our equation, we want to get the r variable on one side, and the constants on one side. First for the variable r, we have 7r on the left side and 1r on the right side. What we can do is subtract 1r from both sides to get rid of the r on the right side of the equation, on the left side, 7r minus r is 6r, and on the right side, r minus r eliminates the r on the right side, and after doing that we have the equation, 6r minus 6 equals 18.

Now we need to get the constants, or numbers without variables on one side of the equation. So, we need to get rid of the -6 on the left side of the equation. To do this, we can add 6 to both sides, on the left side, -6 plus 6 is zero, and on the right side, 18 plus 6 equals 24. Now, we have the equation 6r equals 24. And step 3 is complete, we have all the terms with a variable on one side, and all the terms that do not have a variable on the other side of the equation.

Step 4 is to use division or multiplication to get the variable to have a coefficient of 1. The coefficient is the number in front of the variable, for instance, in our equation, as it is now, it has a coefficient of 6. So, in order to get rid of the 6 in front of the variable, we can divide both side by 6. On the left side, 6r divided by 6 is r, and on the right side, 24 divided by 6 is 4. And we have a solution of r equals 4.

The last step, step 5 is to check the solution. In order to do this, we plug in the solution for the variable into the original equation. In our example of 7r minus 6 equals 3 times the quantity r plus 6 minus 2r, we will plug in the solution of 4 for any r’s in the equation. So, we have 7r, which is 7 times 4, minus 6 equals 3 times the quantity r plus 6, so we will plug in 4 for r in the parenthesis, and the last part of the equation is 2r, which is 2 times 4. Now we have 7 times 4, minus 6 equals 3 times the quantity 4 plus 6 minus, 2 times 4. Which gives us 28 minus 6 equals 3 times 10, minus 8. From that, we get 22 equals 30 minus 8. And from that we get 22 equals 22. So, our solution checks out.

Here are a few more examples on the screen for you, and remember, the key to solving equations like these is to combine like terms and then get the variable on one side and numbers on the other side.
Timestamps
0:00 Intro example equation
0:13 Step 1 remove all parenthesis
0:39 Step 2 combine like terms
0:58 Step 3 get all variables on one side
2:01 Step 4 get variable to have a coefficient of 1
2:27 Step 5 check the solution
3:17 Another example

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