# Solving Inequality Problems

To solve an absolute value equation as $$\left | x 7 \right |=14$$ You begin by making it into two separate equations and then solving them separately.$$x 7 =14$$ $$x 7\, \, =14\,$$ $$x=7$$ or $$x 7 =-14$$ $$x 7\, \, =-14\,$$ $$x=-21$$ An absolute value equation has no solution if the absolute value expression equals a negative number since an absolute value can never be negative.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.

Basically, we still want to get the variable on one side and everything else on the other side by using inverse operations.

The difference is, when a variable is set equal to one number, that number is the only solution.

Quantity of solution at present = 600 liters Quantity of acid in liters in existing solution = 12% of 600 = (12/100) 600 = 72 liters Let "x" be the required quantity of solution to be added.

Acid level in x liters of solution = 30% of x = (30/100)x = 0.3x From this, we come to know that the resulting mixture will contain (600 x) liters solution and (72 0.3x) liters acid.

The following figure shows how to solve two-step inequalities.

Scroll down the page for more examples and solutions.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.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.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?At the link you will find the answer as well as any steps that went into finding that answer.The absolute number of a number a is written as $$\left | a \right |$$ And represents the distance between a and 0 on a number line.The rules for solving inequalities are similar to those for solving linear equations. • Solving One-Step Linear Inequalities in One Variable The solutions to linear inequalities can be expressed several ways: using inequalities, using a graph, or using interval notation.However, there is one exception when multiplying or dividing by a negative number. The steps to solve linear inequalities are the same as linear equations, except if you multiply or divide by a negative when solving for the variable, you must reverse the inequality symbol. Express the solution as an inequality, graph and interval notation.

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