Question

Solve for x algebraically: 7x-3(4x-8) ≤6x + 12-9x7x-3 (4x-8) = 6x +12%-9x7% -12x + 24 = 6x + 12x-9x7x-12x+24 <-3x+125x + 24 =-3x+12-5x+24+3x=12-5x + 3x = 12-24-2x = 12-24-2x = -12,X = 6(b)If x is a number in the interval [4,8], state all integers that satisfy the given inequality.Explain how you determined these values.

Answer 1

Part B.

Given the inequality:

`7x-3(4x-8)\leq6x+12-9x`

Given that the solution to part a is a number in the interval [4, 8], let's state all inetgers that satisfy the given inequality.

Here, we have the interval:

[4, 8]

After solving the inequality, we have the solution:

`x\ge6`

The interval [4, 8] means all numbers from 4 to 8.

Therefore, all numbers in this interval are:

4, 5, 6, 7, 8.

But for this solution we have that x is greater than or equal to 6.

This means it will be 6 or greater but less than 9.

Therefore, the integers that satisfy the given inequality are:

6, 7, 8

ANSWER:

6, 7, 8