A linear equation in one variable has a single unknown quantity called a variable represented by a letter. Eg: ‘x’, where ‘x’ is always to the power of 1. This means there is no ‘x² ’ or ‘x³ ’ in the equation. For example, this linear equation: x + 1 = 4 means that when we add 1 to the unknown value, ‘x’, the answer is equal to 4.
Algorithm for Linear Equations and Inequalities
STEP I : To solve linear equations, you add, subtract, multiply and divide both sides of the equation by numbers and variables, so that you end up with a single variable on one side and a single number on the other side.
STEP II : As long as you always do the same thing to both sides of the equation, and do the operations in the correct order, you will get to the solution.
EXAMPLE : Solve the equation for x
x + 1 = 4
SOLUTION : We have , x + 1 = 4
we need to subtract 1 from both sides of the equation in order to isolate 'x'
x + 1 - 1 = 4 – 1
Now simplifying both sides we have
x + 0 = 3
So, x = 3
EXAMPLE : Solve the equation for x
x + 1 = -3
SOLUTION : We have , x + 1 = -3
We need to subtract 1 from both sides of the equation in order to isolate 'x'
x + 1 - 1 = -3 – 1
Now simplifying both sides we have
x + 0 = -4
So, x = -4
EXAMPLE : Solve the equation for x
-2x = 12
SOLUTION : We have , - 2 x = 12
Step 1. Divide both sides by -2:
- 2 x / 2 = 12 / 2
Step 2. Simplify both sides:
x = -6
Single Step Linear Inequations
In the process of solving an inequation, we use mathematical simplifications which are governed by the following rules:
RULE 1 Same number may be added to (or subtracted from) both sides of an inequation without changing the sign of inequality.
RULE 2 Both sides of an inequation can be multiplied (or divided) by the same positive real number without changing the sign of inequality. However, the sign of inequality is reversed when both sides of an inequation are multiplied or divided by a negative number.
RULE 3 Any term of an inequation may be taken to the other side with its sign changed without affecting the sign of inequality.
EXAMPLE Solve the inequality :
x – 6 > 14
SOLUTION We have ,
x – 6 > 14
x – 6+ 6 > 14 + 6
x > 20
EXAMPLE : Solve the inequality
12 > 18 – y
SOLUTION : We have , 12 > 18 – y
18 – y < 12
18 – y – 18 < 12 –18
– y < –6
y > 6 (multiply both sides by –1 and reverse the sign)
EXAMPLE : Solve the inequality
x + 7 < 15
SOLUTION : We have,
x + 7 < 15
x + 7 – 7 < 15 – 7
x < 8
Related Tags
Study o fSingle Step Linear Equations And Inequalities, What are Single Step Linear Equations And Inequalities?, Help on Single Step Linear Equations And Inequalities