Question

solution:
4 graph the solution set of the inequality ( 3(1 - x) < 9 ).
remember that when you multiply or divide both sides
of an inequality by a negative number, you must reverse
the direction of the inequality sign.

Explanation:

Step1: Expand left side

$3(1-x) = 3 - 3x$
Inequality becomes: $3 - 3x < 9x$

Step2: Add $3x$ to both sides

$3 - 3x + 3x < 9x + 3x$
$3 < 12x$

Step3: Divide by 12

$\frac{3}{12} < \frac{12x}{12}$
$\frac{1}{4} < x$ or $x > \frac{1}{4}$

Step4: Graph setup

• Draw a number line, mark $\frac{1}{4}$ (or 0.25).
• Use an open circle at $\frac{1}{4}$ (since $x$ does not equal $\frac{1}{4}$).
• Shade all regions to the right of $\frac{1}{4}$ (to represent all values greater than $\frac{1}{4}$).

Answer:

The solution to the inequality is $x > \frac{1}{4}$. To graph this:

1. Draw a number line and plot an open circle at $\frac{1}{4}$ (0.25).
2. Shade the entire portion of the number line to the right of this open circle.