# Solving Inequality Problems

But, when a variable is less than or greater than a number, there are an infinite number of values that would be a part of the answer.is less than 4' means that if we put any number less than 4 back in the original problem, it would be a solution (the left side would be less than the right side).The following figure shows how to solve two-step inequalities.

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A manufacturer has 600 litres of a 12 percent solution of acid.

How many litres of a 30 percent acid solution must be added to it so that the acid content in the resulting mixture will be more than 15 percent but less than 18 percent?

Graph: Since we needed to indicate all values less than or equal to 4, the part of the number line that was to the left of 4 was darkened.

Math works just like anything else, if you want to get good at it, then you need to practice it.

An absolute value equation is an equation that contains an absolute value expression.

The equation $$\left | x \right |=a$$ Has two solutions x = a and x = -a because both numbers are at the distance a from 0.Since we are not including where it is equal to, an open hole was used.is greater than or equal to -5' means that if we put any number greater than or equal to -5 back in the original problem, it would be a solution (the left side would be greater than or equal to the right side).On the number line, the positive values go in a reverse or opposite direction than the negative numbers go, so when we take the opposite of an expression, we need to reverse our inequality to indicate this.Graph: Since we needed to indicate all values less than -14, the part of the number line that was to the left of -14 was darkened.Multiplying or dividing both sides by the same positive value does not change the inequality.Graph: Since we needed to indicate all values less than -2, the part of the number line that was to the left of -2 was darkened.Note that the inequality sign stayed the same direction.Even though the right side was a -10, the number we were dividing both sides by, was a positive 5.Graph: Since we needed to indicate all values greater than 3, the part of the number line that was to the right of 3 was darkened.The reason for this is, when you multiply or divide an expression by a negative number, it changes the sign of that expression.