# Open Sentences

Open Sentences are sentences in which an item (number) is missing and has to be supplied to close the sentence.

Example:

3x + 4 = 22, find x

Solution

We subtract 4 from both sides and have 3x + 4 – 4 = 22 – 4 which gives 3x = 18.

Now we can multiply or divide both sides by the same number. Divide both sides by 3 to get:

3x ÷ 3 = 18 ÷ 3

X =6

Example 2:  If 4b + 7 = 9, what is b?

Solution

4b +7 – 7 = 9 – 7

4b = 2

b = 2/4

b = 1/2

Home work: I) if x + 23 = 32     ii) 25 + x =53   iii) if 37 – y = 13, what is y?

Topic: world problems on open sentences

Example 1: I think of a number; if I increase the number 5 times plus 7, the answer is 57, find the number.

Solution

Let the number be x

5x + 7 = 57

5x + 7 – 7 = 57 – 7

5x = 50

Divide both sides by 5

5x ÷ 5 = 50 ÷ 5

:. X = 10

Example 2: A woman is 4 times as old as her daughter, their total age is 50 years. What are their ages?

Let the daughter’s age be x years then the woman’s age 4x years.

X + 4x = 50

5x = 50

X = 50/5

X = 10

:.  The daughter’s age is 10 years and the woman’s age is 40 years.

Home-work:

1. I think of a number, multiply it by 4 and then subtract 7, the result is 21. What is the number?
2. What must be added to 1360 to make 3000?