How to Solve a Linear Equation?

How to Solve Linear Equation

A linear equation is the heart of an algebraic equation in which every term is either a constant or the product of a constant and a single variable. We all know that the linear equations are regularly and frequently in all forms of mathematics and their applications in physics. The reason behind this is because non-linear equations are often well approximated by linear equations.

When a student is asked to solve a linear equation it means to find the value of y for a given value of x. If the equation is of the form y=kx+m, with x and y as variables and k and m as constants, then the equation can be solved in algebraic terms. Therefore, the graphing of this equation will result in a straight line.

To know more about linear equations, here are some simple steps to solve them:

• Suppose you get an equation and it contains fractions, and then use the common denominator to solve the fractions. This can happen if you multiply both sides of the equation by the Least Common Denominator (LCD). Remember, if the equation consists of variables in the denominators of the fractions, then you have to identify the values of the variable which will be divided by zero as you need to avoid these values while solving the equation.
• The second step is to solve both sides of the equation. This will help you in clearing out any parentheses and combining like terms.
• Once you have understood the first two steps, now bring all the variables on one side and the constants on the other.
• Remember that if it’s an integer you have to divide both sides of the equation and if it’s a fraction, you will have to multiply both sides by the reciprocal.
• The last step is to verify your answer. Math is all about getting the right answer in the end. Therefore, after solving the linear equation properly, you have to verify the answer. The right answer will make you more confident about the process and wrong will teach you where you have gone wrong.

Here we have some examples to know more about solving linear equations:

Equation (a): 3(x+5)=2(−6−x)−2x

This equation does not consist of any fraction, so you have to worry about the first step in the process. According to the next step, we will simplify both sides.

3(x+5)=2(−6−x)−2x

3x+15=−12−2x−2x

3x+15=−12−4x

Proceeding to the next step, you will have to bring all the x’s on one side and all the numbers on the other side.

3x+15=−12−4x

3x+15−15+4x=−12−4x+4x−15

7x=−27

Now according to the next step, you have to get a coefficient of 1 in front of the x. Therefore, now we have to divide both sides by 7.

7x/7=−27/7

Answer: x=−27/7

Now as per the last step you can verify your answer and look at the steps once again to confirm you have solved the equation properly.

Equation (b): m−2/3+1=2m/7

As this equation consists of fractions, you have to multiply both sides by the LCD.

21(m−2/3+1)=(2m/7)21

21(m−2/3)+21(1)=(2m/7)21

7(m−2)+21=(2m)(3)

Now, you have to distribute 21 through the parenthesis on the left side of the equation.

7(m−2)+21=(2m)(3)

7m−14+21=6m

7m+7=6m

Answer: m=−7

You can also verify your answer.

−7−2/3+1=2(−7)/7

−9/3+1=−14/7

−3+1=−2

−2=−2

Solved.

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