# Problem solving with linear inequalities

Because we are multiplying by a negative number, the inequalities change direction. Instead of equal signs, though, linear inequalities have inequality symbols much like these: 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 Example: Do not try dividing by a variable to solve an inequality unless you know the variable is always positive, or always negative.

If you can solve linear equations, you can solve linear inequalities. Since I want to give him as little money as possible, I will give him the minimum amount: Remember this – it’s an easily forgotten rule. Then there will be — x left to invest in the safe account.

Now let’s learn how to solve linear inequalities. Well, just look at the number line! Because we are multiplying by a positive number, the inequalities will not change. To solve, we must isolate the variable by adding 5 to both sides. For example, from 3 to 7 is an increase, but from -3 to -7 is a decrease. To tell someone the answer, you would say: You notice that the 2 is on the same side as your variable. You will also learn the notations you need to use when graphing linear inequalities.

Pierre has enough boards and nails. Linear inequalities look very similar. In this lesson, you will learn how similar the solving processes are. This is similar to a mixture word problem , except that this will involve inequality signs, rather than “equals” signs. If you’re seeing this message, it means we’re having trouble loading external resources on our website. But to be neat it is better to have the smaller number on the left, larger on the right.

No matter, just swap sides, but reverse the sign so it still “points at” the correct value! So to move the 2, you subtract it from both sides. But we need to be a bit more careful as you will see. You first solve the inequality by dividing each side of the inequality by Then we divide both sides by 2 so that the variable is by itself.

Recall that a linear equation has variables to the first degree only, and the variables are never squared, cubed, or taken to any other power.

How do we solve something with two inequalities at once? The interest on the business investment, assuming that I get paid back, will be: Practice Let’s try a practice linear inequality: To test a solution, plug it into the inequality and, if the statement remains true, the solution is valid. What Is a Linear Inequality? Your father knows that you’re making these investments in order to pay your child’s college tuition with the interest income.

Multiplying or dividing both sides by a negative number Swapping left and right hand sides Don’t multiply or divide by a variable unless you know it is always positive or always negative.