# Write an absolute value inequality statement for each of the following

Now solve each basic inequality separately. The advantage of the algebraic approach is that solutions are exact, as precise solutions are sometimes difficult to read from a graph.

But 4 will not work, and neither will —4, because they are too far away from zero. Solution: Start by isolating the absolute value quantity add 4 to both sides. I have negative The solution to the given inequality will be the set of all points that are more than two units away from zero. Example 1 Solve each of the following.

## How to solve inequalities with absolute values on both sides

Even 3 and —3 won't work though they're right on the edge , because this is a "less than" but not equal to inequality. Where the solution to an absolute-value equation is points like in the graphic above , the solution to an absolute-value inequality or "inequation" is going to be intervals. The solution to this "greater than" absolute-value inequality is TWO regular inequalities, not one. So if you multiply both sides by 7, you get 2x plus 9 times 7 is 63, is greater than 5. In other words, the solution will be two separate sections: one section being all the points more than two units from zero off to the left, and the other section being all the points more than two units from zero off to the right. Then click the button and select "Solve for x" to compare your answer to Mathway's. Solution: Start by isolating the absolute value quantity add 4 to both sides. The first thing I need to do is clear the absolute-value bars by splitting the inequality into two pieces. To start, I look at the endpoints. To solve, we isolate the variable.

Just graph both of the inequalities on the same number line, as demonstrated in Figure 7. Let's do one more, because I know this can be a little bit confusing.

Nineteen and 24 are five units apart. Due to the nature of the mathematics on this site it is best views in landscape mode. We will illustrate both methods.

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