Solve each inequality. Graph the solution. Show your work.
|7x|+3≤21
To solve the inequality |7x| + 3 ≤ 21, we need to isolate the absolute value term and solve for x.
First, subtract 3 from both sides of the inequality:
|7x| ≤ 18
Next, we can split the inequality into two separate inequalities since the absolute value can result in both positive and negative values:
7x ≤ 18 and -7x ≤ 18
For the first inequality, divide both sides by 7:
x ≤ 18/7
For the second inequality, divide both sides by -7, but remember to reverse the inequality sign:
x ≥ -18/7
So the solution to the inequality is -18/7 ≤ x ≤ 18/7. This means that x can be any value between -18/7 and 18/7, including the endpoints.
Now let's graph the solution on a number line:
-18/7 ------------------------------------ 0 ------------------------------- 18/7
The graph should include a closed circle at -18/7 and another closed circle at 18/7, indicating that x can equal these values. Then, we draw a shaded line between these two points to represent all the values that x can take within this range.