You need to know the value of "x" if you have a problem like 7x – 10 = 3x + 6. An equation like this is called a linear equation, and usually has only one variable. This article will teach you the simple steps.
Step
Method 1 of 2: Start with the Variable on the Opposite Side
Step 1. Look at your problem:
7x - 10 = 3x - 6. A simple linear equation would look like:
Step 2. Check the different terms and constant terms in the equation
The different terms are numbers like 7x or 3x or 6y or 10z, which numbers change depending on the number you put in the variable, or the letter. Constant terms are numbers like 10 or 6 or 30, which will never change.
Usually, equations will not have distinct terms and separate constant terms on opposite sides. In the example above, the left side has different terms and constants, just like the right side
Step 3. Prepare to move the numbers so that the different terms are on one side and the constant terms are on the other, as in 16x - 5x = 32 – 10 (the equation was solved in example 2)
To do this, you may have to subtract or add the numbers you want to move from both sides. In the next step, you will see how to do it in example 1.
Equality 16x - 5x = 32 - 10 indeed has all the distinct terms on one side (left side), while all constant terms are on the other side (right side).
Step 4. Move the different terms to one side of the equation
You can move different tribes to any side.
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In example 1, 7x - 10 = 3x - 6 can be set by selecting to subtract either (7x) or (3x) from both sides. Choosing to subtract 7x, you get:
(7x - 7x) - 10 = (3x - 7x) - 6.
-10 = -4x - 6
Step 5. Next, move all the terms of the constant to the other side of the equation
That is: move the terms of the constant so that the terms are on the opposite side of the equation to the side where the different terms are.
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We see that -6 must be subtracted from both sides:
-10 - (-6) = -4x - 6 - (-6).
-4 = -4x
Step 6. Finally, to find the value of x, just divide both sides by the coefficient of x
The coefficient x (or y, or z, or any other letter) is the number that is in front of the different terms.
- Coefficient x in -4x is -4. So, divide both sides by -4 to get value x = 1.
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Our answer to the equation 7x - 10 = 3x - 6 is x = 1. You can check this answer by plugging 1 back into each x variable and seeing if both sides of the equation have the same number:
7(1) - 10 = 3(1) - 6
7 - 10 = 3 - 6
-3 = -3
Method 2 of 2: Starting from a Variable on One Side
Step 1. Know that sometimes different terms and constant terms are separated
Sometimes, some of your work is already done for you. You already have all the different terms on one side and all the constant terms on the other. If this is the case, all you have to do is do the following.
Step 2. Simplify both sides
For equation 16x - 5x = 32 - 10, we just have to subtract the numbers from each other.
Step 3. Next, divide both sides by the x coefficient
Remember that the coefficient of x is a number in front of different terms.
In this example, the coefficient of x in 11x is 11. The division is 11x 11 = 22 11 to get x = 2. Equation Answer 16x - 5x = 32 - 10 is x = 2.
Warning
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Why do it that way? Try dividing this:
4x - 10 = - 6 like this 4x/4 - 10/4 = -6/4 produce x - 10/4 = -6/4 with lots of fractions to solve, and these equations are not easy to solve; so simplifying is a good reason to collect all the terms of the variable to one side and all the terms of the constant to the other side.
