Solve for xx and graph the solution on the number line below.
minus, 3, is less than, start fraction, x, divided by, minus, 3, end fraction
−3<
−3
x
To solve the inequality \( -3 < \frac{x}{-3} \), first we multiply both sides by -3 to isolate x. However, we have to remember that whenever we multiply or divide both sides of an inequality by a negative number, we must reverse the direction of the inequality sign. Here's how it looks:
\( -3 \times -3 > x \)
\( 9 > x \)
Now we have the inequality \( 9 > x \), which also can be written as \( x < 9 \). This means x can be any value less than 9.
To represent this on a number line, you would draw a number line with an open circle at 9 to indicate that 9 is not included in the solution, and you would shade everything to the left of 9 to show that all numbers less than 9 are included.
Since I cannot physically draw on this platform, please visualize the following:
Imagine a horizontal line with numbers marked at regular intervals. At the number 9, there's an open circle (indicating that 9 is not part of the solution). Then, a shaded line extends from this open circle to the left, continuing indefinitely, representing all numbers less than 9. This shaded part of the line expresses the solution set for the inequality \( x < 9 \).