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Three Main Rules
A linear equation is any two expressions (like “3x+2" or “54") set equal to each other, assuming that none of the variables in the equation are raised to a power higher than 1. For example, “4x+8=29" is a linear equation, but “5x^4=100" is not a linear equation, because the variable “x" is raised to the power of “4."
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Just remember these three rules of solving linear equations, and you’ll be successful every time. Remember to follow the order of the steps correctly. The purpose of these steps is to “isolate the variable," or to get the variable alone on one side of the equation.
1. Simplify each side of the equation.
2. Add or subtract terms so that the variable is on one side of the equation and all the other terms are on the other side.
3. Multiply or divide any values in front of the variable, as needed.
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Simple As 1-2-3
Now let’s try to solve a linear equation so you can see how the steps work. Let’s try this linear equation, which seems a bit complicated at first:
3(x + 4) = 45
Step 1: Simplify each side of the equation. In this case, only the left side of the equation needs to be simplified. In this case, you can use the distributive property of multiplication to change “3(x + 4)" into “3x + 12." So the new equation would read “3x + 12 = 45."
Step 2: Add or subtract terms. To get the variable alone on the left side of the equation, you have to get rid of the “12." To do that, you can subtract 12 from both sides of the equation. So the new equation would read “3x = 45 – 12" or “3x = 33."
Step 3: Multiply or divide values in front of the variable. To get the variable alone on the left side of the equation, you have to get rid of the “3." To do that, you can divide 3 from both sides of the equation. So the new equation would read “x = 33/3," or “x = 11."
There’s your answer! The value of x is 11.
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How to Check Your Answer
Checking your answer in an linear equation is easy. Just plug the new value of the variable into the equation. For example, in this equation, you would just substitute 11 for any x in the equation. It would look like this:
3(11 + 4) = 45
11 + 4 = 15, and 3 X 15 = 45. It worked! We got the correct answer in solving this linear equation.