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Online Quiz (Worksheet A B C D)

Questions Per Quiz = 2 4 6 8 10

High School Mathematics
1.19 Linear Equations - One Variable

  • An equation is an equality connecting with some unknowns.
  • The unknowns are represented by letters and are called variables.
  • If the equation has only one unknown, it is called an equation with one variable.
  • The word Linear means of degree one.

Example:
Divide 64 into two parts such that three times the greater part will be equal to five times the smaller one.
Solution:
Let x be the greater part. Then 64 - x is the smaller part.
Then 3x = 5(64 - x)
3x = 320 - 5x
3x + 5x = 320
8x = 320
The two parts are 40 and 24.

Example:
Find a number such that one-fourth of it is less than one-third of it by 4.
Solution:
Let the number be x.
One-fourth of it is less than one-third of it by 4: x/4 + 4 = x/3
x/4 + 4 = x/3
x/4 + 4 = x/3
(x+16)/4 = x/3 ---- multiplying both sides by 12 we have
12 ((x+16)/4) = 12 (x/3)
3x + 48 = 4x
3x + 48 - 3x = 4x - 3x
48 = x
The number is 48.


Directions: Solve the following linear equations. Also write at least 10 examples of your own.
Q 1: Divide 15 into two parts so that six times the smaller number is equal to five times the larger number plus 2. Find the numbers.
7 and 8
4 and 11
6 and 9

Q 2: Divide 9 into two parts so that thrice the smaller number is equal to twice the larger number plus 2. Find the numbers. (Hint: Let x be the smaller number. Then the larger number is 9-x. The equation can be written as 3(x) = 2 (9-x) + 2. Find x and 9-x)
7 and 5
4 and 5
4 and 6

Q 3: Find a number such that one-third of it is less than one-half of it by four.
30
24
26

Q 4: Divide 17 into two parts so that six times the smaller number is equal to five times the larger number plus 3. Find the numbers.
7 and 10
6 and 11
8 and 9

Q 5: Find a number such that one-half of it is more than one-third of it by 3.
18
12
11

Q 6: Find a number, if half of which when added to 3, is equal to 12 diminished by 1/4 th of that number. (Hint: Algebraic equation can be written as x/2 + 3 = 12 - x/4 )
40
12
10

Q 7: Find a number such that one-fourth of it is less than one-third of it by 3.
33
42
36

Q 8: Divide 25 into two parts so that six times the smaller number is equal to four times the larger number. Find the numbers.
11 and 14
10 and 15
9 and 16

Question 9: This question is available to subscribers only!

Question 10: This question is available to subscribers only!


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