## Multi-step inequalities

Direction: Which way the arrow "points". When we swap the left and right hand sides, we must also change the direction of the inequality :.

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We can often solve inequalities by adding or subtracting a number from both sides just as in Introduction to Algebra , like this:. And that works well for adding and subtracting , because if we add or subtract the same amount from both sides, it does not affect the inequality.

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Example: Alex has more coins than Billy. If both Alex and Billy get three more coins each, Alex will still have more coins than Billy. No matter, just swap sides, but reverse the sign so it still "points at" the correct value!

Note: "x" can be on the right, but people usually like to see it on the left hand side. So, what do we do on these? Our goal is the same: Get the x alone!

## Solve an Inequality

Let's go: Get the x alone in the middle But, what does this mean? Accept All Cookies.

Accept First Party Cookies. Solving Inequalities Sometimes we need to solve Inequalities like these: Symbol.

Some things can change the direction! Multiply or divide both sides by a negative number Swapping left and right hand sides. But it is normal to put "x" on the left hand side Well, just look at the number line! When multiplying or dividing by a negative number, reverse the inequality.

Because we are multiplying by a positive number, the inequalities will not change. When we multiply or divide by a negative number we must reverse the inequality.