Expressions are formed by variables and constants.
Variable don't have a fixed value and usually represented by letters (x, y, n, m, s)
Constants have fixed value and are represented by numbers(5, 9, 7, -5, 1/2)
Practical Usage of Expressions
1. 7 added to n = 7 + n
2. 7 subtracted from n = 7 - n
3. n multiplied by 7 = 7n
4. n divided by 7 = n / 7
Sara´s present age is x years.
What will her age be 10 years from now? x + 10
What was her age 3 years back? x -3
Sara´s cousin is 3 times her age : 3x
Sara´s sister is 2 years younger than her cousin : 3x – 2
Sara´s brother is 4 years older than her cousin: 3x + 4
Write the expression:
1. George is 3 years older than Ravi. Let´s say Ravi is x years old. So George is years old. |
2. My age is 2 years more than 5 times my cousin´s age. Let´s say my cousin´s is n years old. So my age is |
3. Length of a park is 4 mts less than the breadth (b) of a park. What is the length (l) of the park? The length of the park is mts. |
4. My age is 3 years less than 4 times my cousin´s age. Let´s say my cousin´s is m years old. So my age is |
Equations: are expressions in which the value of
Left hand side(LHS) = Right hand side (RHS)
It cannot have > or <
Write if the expression is an equation with Yes (Y) or No (N)
1. 17 = x + 7 |
2. t – 7 > 5 |
3. 4 / 2 = 2 |
4. 2m < 5 |
5. 4x = 2 |
2 types of Equations:
Variable Equations Numerical Equations
Equations with variables in them Equations with only numbers and no variables
Example: 2n = 10 Example: 8 - 3 = 5
x - 2 = 0 20 - (10 -5) = 15
Complete the table and find the solution of x/3 = 4
x
8
9
10
11
12
13
14
15
16
x/3
8/3
9/3
10/3
11/3
12/3
13/3
14/3
15/3
16/3
x/3
2
2 ___
3
3
1
3 ___
3
2
3 ___
3
4
1
4 ___
3
2
4 ___
3
5
1
5 ___
3
So the solution of x/ 3 = 4 is 12 (x = 3* 4)
Solving Equations
Adding, Subtracting, Multiplying or dividing on both sides
Example
1. x + 3 = 5
x + 3 – 3 = 5 – 3
x + 0 = 2
x = 2
****************************
2. x – 5 = 10
x –5 +5 = 10 + 5
x + 0 = 15
x = 15
****************************
3. 3n = 6
3n 6
___ = ___
3 3
n = 2
****************************
4. p
___ = 4
7
7p 4* 7
____ =
7
p = 28
****************************
5. 3s = 10
__
10
10 * 3s = 10 * 10
___
10
3s = 100
3s = 100
_____ ____
3 3
Adding, Subtracting, Multiplying or dividing on both sides
1. Since we have a positive constant we are going to add a negative constant to cancel them out.
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2. Since we have a negative constant we are going to add a positive constant to cancel them out
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3. We divide both sides with a constant which is multiplied to a variable.
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4. This is a division problem. so we are going to multiply with the constant with which the variable is divided
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5. This problem involves multiplication and division so we are going to divide and multiply)
Transposing
1. x + 3 = 5
x = 5 – 3
x = 2
***************************
2. x – 5 = 10
x = 10 + 5
x = 15
***************************
3. 3n = 6
n = 6
___ = 2
3
n = 2
***************************
4 . p
___ = 4
7
p = 4* 7
p = 28
****************************
5. 3s
____ = 10
10
3s = 10 * 10
3s = 100
s = 100
____
3
when the constant changes the side , it changes its sign too.
1. the positive constant when moved to the other side of the equal changes into a negative constant
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2. the negative constant when moved to the other side of the equal changes into a positive constant
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3. If it is multiplication , then the constant is divided with the constant of the variable.
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4. If it is division , then the constant is multiplied with the constant of the variable.
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5. This problem involves multiplication and division so we are going to divide and multiply)
4(m + 3) = 8
4m + 12 = 8
4m = 8 -12
4m = -4
m = -1
4 = 5(p -2)
4 = 5p -10
4 + 10 = 5p
14 = 5p
14
__ = p
5
7m + 19 = 13
2
7m = 13 – 19
2
7m = 26 -19
2
7m = 7
2
m = 7
2
7
1 (It is assumed)
= 7 * 1 = 7 = 1
2 7 14 2
-4 (2 + x) = 8
– – = 8
– = 8 +
– =
– x =
—
x = –
4 + 5 (p – 1) = 34
4 + – = 34
4 + = 34 +
= 34 + –
=
p =
/
p =
2b
/
3
– 5 = 3
2b
/
3
= 3 +
2b = 3 (3 + )
2b = ( )
2b =
b =
/
b =
0 = 16 + 4(m – 6)
0 = 16 + –
0 = + m
= m
m =
/