Question

Please help me solve this. Solve the inequality 5 - x < -9 and illustrate the solution on a number line.

i) If x is a prime number, write down the smallest possible value of x that satisfies the inequality.
ii) Given that x is a perfect cube, find the smallest possible value of x.

Answer 1

To solve the inequality 5 - x < -9, subtract 5 from both sides, multiply by -1 and flip the inequality sign, giving x > 14. The smallest possible value of x that satisfies the inequality when x is a prime number is 17, and when x is a perfect cube is 27.

Step-by-step explanation:

To solve the inequality 5 - x < -9, we need to isolate the variable x.

We can start by subtracting 5 from both sides of the inequality:

5 - x - 5 < -9 - 5

Simplifying, we get:

-x < -14

Now, to isolate x, we need to multiply both sides of the inequality by -1 and flip the inequality sign:

-x(-1) > -14(-1)

This gives us:

x > 14

So the solution to the inequality is x > 14. Now, let's plot this solution on a number line:

i) If x is a prime number, the smallest possible value of x that satisfies the inequality is 17, since it is the smallest prime number greater than 14.

ii) If x is a perfect cube, the smallest possible value of x that satisfies the inequality is 27, since it is the smallest perfect cube greater than 14.