4 pencils and 6 pencils give 10 pencils.
7 boys and 5 girls give in primary 5 give 12 pupils.
These statements can be written mathematically as:
4 pencils + 6 pencils = 10 pencils
7 boys + 5 girls = 12 pupils
Example 1
⃞ + 3 =14
21 - ⃞ = 6
4
3 x ⃞ = --------
3
⃞ ÷ 14 = 2
Solution
This means,the empty boxes represent the unknown numbers.The empty boxes can be then replaced with letters,thus the statement above could be written as:
y + 3 =14
21 - x = 6
4
3p = --------
3
u ÷ 14 = 2
From the above explanations,we can see that the highest power of unknown variables/numbers is (1), i mean ( x)¹.
Examples of clearing the bracket to form equation and collecting like terms
Solve the following equations.(a) 3(4y - 1 )= 27
(b) 2(x + 5 ) - 12 = 4
(c) 5x - 3(3x - 1 ) = 39
Scope: The equations contain brackets. To operate them, we first open the brackets ,let goo...
(a) 3(4y - 1 )= 27
12y - 3 = 27 ( brackets opened.)
Add 3 to both sides.
12y - 3 + 3= 27 + 3
12y = 30
Divide both sides by 12.
12y 30
--------- = -----------
12 12
1
y =2 ---------
2
Check:
3(4y - 1 )= 27
5
3(4 x ------ - 1 ) = 27
2
3 ( 10 - 1 ) = 27
3 x 9 = 27
27 = 27
That good, you can see how i manipulate the variables.To solve the above equations,clear the brackets first to form an equation.After that, you add others elements,to check you substitute the letters with number.
(b) 2(x + 5 ) - 12 = 4
2x + 10 - 12 =4 (brackets opened)
2x - 2 = 4
Add 2 to both sides.
2x - 2 + 2 = 4 + 2
2x = 6
Divide both sides by 2.
2x 6
------- = --------
2 2
x = 3
Check:
2(x + 5 ) - 12 = 4
2 ( 3 + 5 - 12) = 4 ( BODMAS)
2 x 8
16 - 12 = 4
4 = 4
(c) 5x - 3(3x - 1 ) = 39
5x - 9x + 3 = 39
4x + 3 = 39
subtract 3 from both sides .
4x + 3 - 3 = 39 - 3
4x = 36
Divide both side by 4.
4x 36
-------= ---------
4 4
x = 9
Example 2
Now let look at this particular one that have 2 brackets to be cleared.
Solve these:
(i) 5(r - 1 ) + 4( (r + 2) = 75
5r - 5 + 4r + 8 = 75 ( Brackets cleared.)
5r + 4r - 5 + 8 ( collecting like terms.)
9r +3 = 75
Subtract 3 from both sides.
9r +3 - 3 = 75 - 3
9r = 72
Divide both by 9.
9r 72
--------- = -----------
9 9
r = 8
Check:
5(r - 1 ) + 4( (r + 2) = 75
5(8 -1) + 4(8 +2) = 75
40 - 5 + 32 + 8 =75 -----we have opened the bracket
35 + 40
75 = 75 .... a balance equation.
Now solve the following:
(a) 4(x + 6) - 3x = 25
(b) 1 + 3(y - 1) =4
(c) 7k - (2 - k) = 0
(d) 3(2a + 1 ) + 2(a -1 ) =-23
If you have questions,put them in the comments box.
){kind=link}
0 Comments