Step-By-Step Guide to Solving Linear Equations

A linear equation is an algebraic expression that expresses equality between two sides of the expression with a given unknown. It is primarily an algebraic sentence that tends to establish the value of one given unknown in the form x + 3 = 2 you will notice that in the statement or sentence x + 3 = 2, there are two sides to the sentence:

The first is x + 3 (this is the left hand side – LHS) and

The second is 2. (This is the right hand side – RHS)

The equal to sign (=) is what separates the two sides of the algebraic sentence.

Step by step guide to solving linear equations.

When a linear equation is given, the following steps are taken to solve it and get the value of the unknown.

1.   Identify the unknown to be solved for. If, for instance we have x + 3 = 7 - x, the unknown to be solved for is x.

2.   Identify the like terms in the equation. In the above equation (x + 3 = 7 - x), for instance, 3 and 7 are like terms so also are x and -x.

3.   Bring like terms together. If you have an equation as x + 3 = 7 – x, x and –x will come together while 3 and 7 will come together.

4.   When bringing like terms together, remember that when a positive sign (+) crosses the equality sign (=), it changes to negative sign (-) and when a negative sign (-) crosses the equality sign (=), it changes to positive sign (+)

5.   After this, simplify the terms as applicable.

6.   Divide both sides by the coefficient of x if the coefficient is not equal to 1

Example1

Solve for x in the following algebraic sentence x + 3 = 7 – x

Solution

Given the equation x + 3 = 7 – x

The like terms in the equation x + 3 = 7 – x  are x,-x and 3,7

Thus, we say collect like terms or bring like terms together as follows

x + x = 7 – 3

2x = 4

Coefficient of x is 2. Divide both sides by 2 as follows

^2x/₂ = ⁴/₂

x = 2

Note: This means that the algebraic sentence x + x = 7 – 3 is true when x = 2

Checking for Correctness

It is necessary to learn how to check if the answer to an algebraic sentence is correct. To do this, we simply substitute the value of the unknown into the equation (sentence) to see if the left hand side (LHS) equals the right hand side of the equation.

Example

Check if x=2 is correct for the equation x + 3 = 7 – x 

Checking:

LHS      x + 3

       = 2 + 3

         = 5

RHS     7 – x 

                       = 7 – 2

  = 5 (same as LHS)

With this, we say that x = 2 is correct for the equation x+3=7–x