5 Tricks for Solving Linear Equations

Linear equations are equations that have the form ax + b = 0, where a and b are constants. Solving linear equations is an important skill in a variety of fields, including mathematics, science, and engineering.

In this blog post, we will explore five tricks for solving linear equations:

Isolate the variable

The first trick for solving linear equations is to isolate the variable on one side of the equation.

To do this, we need to move all the terms that do not contain the variable to the other side of the equation.

For example, consider the equation 3x + 5 = 12.

To isolate the variable x, we can subtract 5 from both sides of the equation to get:

Now, we can divide both sides of the equation by 3 to solve for x:

Use the distributive property

The distributive property states that for any numbers a, b, and c, a(b + c) = ab + ac. This property can be used to simplify linear equations by distributing the coefficient of the variable over the terms on the other side of the equation.

For example, consider the equation 2(x + 3) = 10. We can use the distributive property to simplify this equation as follows:

Combine like terms

Sometimes, linear equations will have multiple terms on one or both sides of the equation. In these cases, it can be helpful to combine like terms (i.e., terms that have the same variable and coefficient) in order to simplify the equation.

For example, consider the equation 3x + 2x + 4 = 10. To solve this equation, we can first combine the like terms to get:

Use inverse operations

Inverse operations are operations that undo each other. For example, the inverse of addition is subtraction, and the inverse of multiplication is division. We can use inverse operations to isolate the variable in a linear equation by undoing the operations that have been performed on the variable.

For example, consider the equation 3x / 6 = 5.

To solve this equation, we can use the inverse of division (which is multiplication) to isolate the variable:

Check your solution

Finally, it is always a good idea to check your solution to make sure it is correct. To do this, simply plug your solution back into the original equation and see if it satisfies the equation.

If it does, then your solution is correct.

If not, then you may have made a mistake somewhere and you will need to go back and try again.

In conclusion, there are several tricks that can be used to solve linear equations, including isolating the variable, using the distributive property, combining like terms, using inverse operations, and checking your solution.

By using these tricks, you can solve linear equations quickly and accurately.