inequalities

Inequality is a collection of operators which is used to represent the inequality of algebraic equations. An inequality is a statement of algebraic expression to calculate the value of unknown variables. In general aspect we can say that inequality is used to calculate the algebraic expression that is not same in both sides of equal sign. The term inequality can be applied to any type of statement by using the various types of symbol like ‘>’ (greater then), ‘<’ (less then), ‘<=’ (less then equal to), ‘>=’ (greater then equal to) and so on. The concept of inequality helps the students of Grade VII to understand basic concepts of mathematics.
Here we show you the fundamental properties of inequalities to understand the concept of inequalities:
a)      x, y and z are the real numbers if x ≤ y then x + z ≤ y + z.
b)      x, y and z are the positive real numbers if x ≤ y then xz ≤ yz.
A solution of an inequality is a number which is substituted for the variable makes the inequality a true statement. In the mathematics there are various properties defined for inequality to solve equations. In the next session we are going to discuss Multistep problems.
a) Transitive property: if a > b and b > c then a > c.
b) Addition property: if a > b then a + c > b + c.
c) Multiplication property: if a > b then ab > ac.
d) Subtraction property: if a > b then a – c > b – c.
The above given properties of inequality helps the students to Graphing inequalities into the graph. Inequalities can be performed by solving the inequalities into the algebraic expressions. There are some rules given below:
a)      Adding and subtracting the same number on both sides.
b)      After performing the above rule interchange the sides and changing the orientation of the given inequality symbols.
c)      If needed, then perform the multiplication and division of same positive or negative number on both sides of equal sign then changing the orientation of the inequality symbol.

In the next session we are going to discuss Multistep problems. 

Multistep problems

In this unit we are going to learn how to solve multistep problems. This unit is designed for Grade VII.  When we have certain equations, which are having one variable, we proceed in the way that in every step, we move towards separating all constant values from the variables. This can be done in single steps, when the equations are small. But in the bigger equations which include multi operators existing in the equation, can be solved step by step. In the initial step, we will first shift all the variables to one side of the equation. While shifting we must remember that the positive term changes to a negative term and the negative term changes to a positive term. Here we can do the same process in another way, if the term which is negative on the right side of the equation has to be shifted to the right side of the equation, and then we simply add positive value of the same term on the both side of the equation. Thus the positive and the negative term of the right side of the equation will be cancelled, on another hand the positive of the same value will be added to another side of the equation.

We can proceed in the same method for subtraction too. Thus any negative value from one side of the equation is to be removed, for this we will add the same value on the both sides of the equation. This becomes possible as the addition and the subtraction are inverse of each other.

 Now we look at multiplication and division sign which appears in the equation. To separate the variable, we need to see that the constant value with the variable consists of the multiplication operator or the division operator. If the operator is of multiplication, divide both sides of the equation by the same number and if the operator is of division, multiply both sides of the equation by that number. It will give the resultant value of the variable.

In the next session we are going to discuss Geometry. 

 

Multistep Problems in Grade VII

Algebra! Who invented this boring branch of mathematics. Many students usually ask this question. But my dear students I am here to take your pain and to make this boring subject an interesting one for you. Whenever you deal with any math problem try to understand the problem behind the concepts and relate it with the real life problems then surely friends you will understand the problem properly. Now, move towards the today’s topic that is multistep problems in grade VII. What do you understand by the term multistep problems? As the name says multistep, you easily understand its concept that multistep means multiple step and by multistep problems we mean that how to solve problems involving different steps.

In multistep problems, a problem is solved in different steps and each and every step is very important. If you solve any problem and if any of its step is wrong then you won’t get the final answer right. In such type of problems each and every step must be right otherwise the output will be wrong even a minute mistake can cause problem to your answer. so be careful whenever you solve these types of problems and check and all the steps properly and carefully. The multistep problems can be in any form like they can be in equation form or word problem form.

Let’s take an example and understand the problem properly.  

First take an example of equation which is solved in multistep.

Example: Solve the given equation for the variable q

20 = 3(2 q + 8) + 4

Answer:

-20 = 3 (2q + 8) + 4

Eliminate the parentheses,

-20 = 3 (2 q) + 3 (8) + 4

-20 = 6q + 24 + 4

-20 = 6q + 28

Subtract 28 on both sides of the equation

-20 - 28 = 6q + 28 – 28

-48 = 6q

Divide by 6 on both sides of the equation

-48/6 = 6q/6,

-8 = q

This is the final answer of the equation.

 

 

Now, here is an example of the same but the form of word problems.

Question: Allen earns a base salary of $94 per week with a commission of 14% of sales. if she had $100 in sales last week, then find her total pay.

Solution: as you all know the formula to calculate commission and total pay.

Commission = commission percentage x sales,

Total pay = base salary + commission.

First calculate the commission. For this we can use the first formula

Commission = commission percentage x sales,

= 14 % x 100

= 14 /100 x 100,

= 14.

so the commission is $14.

Now we can easily calculate the total pay, using second formula,

total pay = base salary + commission,

= 94 + 14,

= 108,

The total pay was $108.  

in this the simple way to solve multistep problems only take care that all the calculations and formula used are right or not, then you can easily solve all the different problems.