RTCNTC said:Solve the inequality.
| (4 - 5x)/2 | > 1
Can I use the following theorem?
If a > 0, then | u | > a if and only if u < -a or u > a
An inequality is a mathematical statement that compares two quantities and uses symbols such as <, >, ≤, or ≥ to show which quantity is larger or smaller. Unlike equations which have an equal sign, inequalities have a range of possible solutions.
To solve an inequality, you must isolate the variable on one side of the inequality sign. This can be done by using inverse operations, just like solving an equation. Remember to reverse the direction of the inequality sign if you multiply or divide by a negative number.
The three main types of inequalities are linear inequalities, quadratic inequalities, and rational inequalities. Linear inequalities involve a linear expression on one side of the inequality sign. Quadratic inequalities involve a quadratic expression on one side. Rational inequalities involve a rational expression on one side.
An open circle on a number line represents a number that is not included in the solution of the inequality. A closed circle represents a number that is included in the solution. This is important to note when graphing solutions on a number line.
Yes, inequalities with multiple variables can be solved by isolating one variable on one side of the inequality sign and then using substitution to solve for the remaining variables. It is important to keep track of the inequality sign and any restrictions on the variables. Graphing the solution in the coordinate plane can also help visualize the solution.