Question

The sum of a number and 3 is less than 10 if x denotes the number what would be the possible values of x

x>13
x<13
x>7
x<7

Answer 1

Let the number be x

The sum of number and 3

• x+3

Is less than 10

• x+3<10

Lets solve it

• x<10-3
• x<7

Hence

Option D is correct

Answer 2

x<7

Explanation:

Consider the number x (as mentioned in the question). Now carefully pay attention to the given condition

⇒"The sum of a number and 3 is less than 10"

Remember the notation of the term "less than" in mathematical context is indicated by "<" sign. Hence our inequality is

⇒ x+3<10

adding or subtracting any number from the both sides of an inequality DOESN'T change its direction. Thus, if we cancel out 3 from both sides it won't swap the inequality. Therefore

⇒ x+3-3<10-3

⇒
`x<7`

In terms of interval notation


`\implies x\in( -\infty,7)`

In conclusion

The answer is D)
`x < 7`