I can definitely help you with that!
(i) To solve for x in the inequality 8 → x < 5x + 2, you want to isolate x on one side of the inequality. Here's how you can do it step-by-step:
8 → x < 5x + 2
Subtract 5x from both sides to get x alone on one side:
8 - 5x < x + 2
Subtract x from both sides to have all x terms on one side:
8 - 6x < 2
Now, subtract 8 from both sides to isolate the x term:
-6x < -6
Finally, divide by -6 (remember when dividing by a negative number, flip the inequality sign) to find the solution:
x > 1
(ii) To show this solution on a number line with markings for 4, 3, 2, 1, 0, -1, -2, -3, -4, follow these steps:
- Draw a number line with marks for 4, 3, 2, 1, 0, -1, -2, -3, -4.
- Since x > 1, mark an open circle on the number 1 to indicate that it is not included in the solution.
- Draw an arrow to the right of the number 1 to show all the numbers greater than 1 are solutions to the inequality.
This representation on the number line visually shows that x is any real number greater than 1 but does not include the number 1 itself.
