Question

1. consider the inequality: 4x + 8 < 10x - 10.

12a solve the inequality.
x > 3
12b now, plot the inequality 4x + 8 < 10x - 10 on the number line below.

Explanation:

Step1: Move x - terms to one side

$4x+8<10x - 10$ becomes $4x-10x<-10 - 8$.

Step2: Simplify both sides

$-6x<-18$.

Step3: Solve for x

Dividing both sides by - 6 (and reversing the inequality sign since dividing by a negative number), we get $x > 3$.

For 12b:
On the number - line, we draw an open circle at $x = 3$ (because $x>3$, 3 is not included) and shade the line to the right of 3 to represent all the values of $x$ that satisfy the inequality.

Answer:

12a. $x>3$
12b. Draw an open circle at 3 on the number - line and shade to the right.