Question

State all integer values of a in the interval -2 ≤ x ≤ 4 that satisfy the following

inequality:
-5x+5 ≥7

Answer 1

Answer: -2 and -1

Step-by-step explanation

Solve for x:

`-5\text{x}+5 \ge 7\\\\-5\text{x} \ge 7-5\\\\-5\text{x} \ge 2\\\\\text{x} \le 2/(-5)\\\\\text{x} \le -0.4\\\\`

Note the inequality sign flips when we divide both sides by a negative number.

If x is an integer, then the largest x can be is x = -1, which means x can be any of these values: {..., -4, -3, -2, -1} where the three dots means the pattern continues on to the left forever. If it might help, then you can think of it like this: {-1, -2, -3, -4, ...} but it's of course not the standard way to sort negative numbers.

Now we're told that -2 ≤ x ≤ 4 which when combined with the set above, gets us the answer {-2, -1}

If we replaced x with -2, then,

-5x+5 ≥7

-5(-2)+5 ≥7

10+5 ≥7

15 ≥7

which is true and confirms x = -2 works. I'll let you try out x = -1.