Solving two steps Inequalitites
A mathematical statement consisting of two expressions which are separated by an equal to sign is called an equation. Here the expressions on either side of the equal to sign have the same value. Either of the expressions or both the expressions may consist of a variable.
The method of manipulating the equation using the various mathematical operations to find the value of the variable is solving the equation.
Let us learn the steps involved in solving two steps equations, here two steps are used in finding the value of the variable in the equation.
Consider the example, solve 3x-2= 7.
Step1: Add 2 on both sides,
3x-2+2= 7+2
3x = 9
Step2: dividing on both sides with 3
3x/3 = 9/3
x=3 is the solution
Solving two equations involves a different method. They can be solved using one of the following methods:
In the substitution method, one of the equations is written in terms of one variable whose value is substituted in the second equation and solved.
This value is again substituted in one of the equations to arrive to the value of the second variable. In elimination method one of the variable term is eliminated by making the terms same with opposite sign and then solved for the variable.
This value is substituted in one of the equations to arrive to the value of the second variable. In the graphing method the graphs of both the equations are plotted and the point of intersection of the lines would be the solution set.
When two values are not equal then we call the relationship between them as inequality. The inequalities are ‘greater than’ represented by the symbol ‘>’, ‘less than’ represented by ‘<’, ‘greater than or equal to’ represented by ‘≥’ and ‘less than or equal to’ represented by ‘≤’. In this relationship unlike the ‘equal to’ relationship the variable can have number of solutions. Let us now Solving Two Step Inequalities using a simple example problem.
Solve 6x – 4 > 38 using two steps.
Step1: Adding 4 on both sides to eliminate 4 on the left hand side of the inequality
6x – 4+4 > 38 +4
6x> 42
Step2: Dividing on both sides by 6 to isolate the variable ‘x’
6x/6 > 42/6
x>7 which means ‘x’ can take all the values greater than 7
One important point to remember while solving inequalities is that the sign of inequality changes when the whole inequality is multiplied or divided by a negative number.
The method of manipulating the equation using the various mathematical operations to find the value of the variable is solving the equation.
Let us learn the steps involved in solving two steps equations, here two steps are used in finding the value of the variable in the equation.
Consider the example, solve 3x-2= 7.
Step1: Add 2 on both sides,
3x-2+2= 7+2
3x = 9
Step2: dividing on both sides with 3
3x/3 = 9/3
x=3 is the solution
Solving two equations involves a different method. They can be solved using one of the following methods:
- substitution method,
- elimination method
- graphing method.
In the substitution method, one of the equations is written in terms of one variable whose value is substituted in the second equation and solved.
This value is again substituted in one of the equations to arrive to the value of the second variable. In elimination method one of the variable term is eliminated by making the terms same with opposite sign and then solved for the variable.
This value is substituted in one of the equations to arrive to the value of the second variable. In the graphing method the graphs of both the equations are plotted and the point of intersection of the lines would be the solution set.
When two values are not equal then we call the relationship between them as inequality. The inequalities are ‘greater than’ represented by the symbol ‘>’, ‘less than’ represented by ‘<’, ‘greater than or equal to’ represented by ‘≥’ and ‘less than or equal to’ represented by ‘≤’. In this relationship unlike the ‘equal to’ relationship the variable can have number of solutions. Let us now Solving Two Step Inequalities using a simple example problem.
Solve 6x – 4 > 38 using two steps.
Step1: Adding 4 on both sides to eliminate 4 on the left hand side of the inequality
6x – 4+4 > 38 +4
6x> 42
Step2: Dividing on both sides by 6 to isolate the variable ‘x’
6x/6 > 42/6
x>7 which means ‘x’ can take all the values greater than 7
One important point to remember while solving inequalities is that the sign of inequality changes when the whole inequality is multiplied or divided by a negative number.