Question

Sketch the graph of the inequality. $$4 x<-12$$

Short answer

The solution to the inequality \(4x < -12\) is \(x < -3\). All values less than -3, not including -3 itself, are valid. This is graphically represented by an open circle above the -3 on your number line with an arrow pointing left.

Step-by-step solution

Solve the Inequality

Firstly, isolate the variable on one side of the inequality to find its value. This is done by dividing each side of the inequality by 4. Therefore, \(x < -12/4\), and thus, \(x < -3\).

Draw a Number Line

Draw a line representing all possible values of x, known as a number line. Make sure you include -3 on your number line. It can be placed anywhere on the line, but usually, it is best to put it in the middle, if possible.

Represent the Solution on the Number Line

Since the inequality does not include the value -3, represented by < rather than ≤, put an open circle above the -3 on your number line to show that -3 is not part of the solution. Then draw an arrow pointing to the left, indicating that the solution for x includes all numbers less than -3.