Question

Priya looks at the inequalities 12-X>5 and says " I subtract a number from 12 and wants a result that is bigger than 5. That means that the solutions should be values of x that are smaller than something. "

Do you agree with priya? Explain your reasoning and include solutions to the inequality in your explanation.

​

Answer 1

Yes, i agree with Priya, the solutions is values of x that are smaller than 7.

Explanation:

Given the inequality is

12 - X > 5

Solution

12 - X > 5

-x > 5 - 12

-x > -7

x < 7 (due to change in sign of x, change the sign of inequality)

It means all integers smaller than 7.

Prove

put values to check if equation hold the solution

domain = -∞ < x < 7

1)

12 - X > 5

12 - 5 > 5

7 > 5 TRUE

2)

12 - X > 5

12 - 1 > 5

11 > 5 TRUE

3)

12 - (-80) > 5

12 + 80 > 5

92 > 5 TRUE

Hence, range = y > 5.