BeckyRN said:Homework Statement
The Questions are 2x - 3 > x + 15
-4 x = 2 < 10 ( I am not sure how to place a line under the < on my computer)
and -5x + 1 < -2x + 10
Inequalities refer to mathematical statements that compare two quantities or expressions. They use symbols such as <, >, ≤, and ≥ to show a relationship between the quantities, with one being greater than, less than, or equal to the other.
To solve an inequality, you need to follow the same rules as solving equations, but with one key difference. Whenever you multiply or divide both sides of the inequality by a negative number, you must flip the direction of the inequality symbol. For example, if you have -2x < 6, dividing both sides by -2 would give you x > -3.
Inequalities are used in various real-life situations, such as in determining who qualifies for government assistance, setting income and salary levels, and deciding on the minimum and maximum speed limits for roads. They are also used in business and economics to represent supply and demand, profit and loss, and budget constraints.
Yes, inequalities can be graphed on a number line or a coordinate plane. To graph an inequality, you need to first solve it for y (if it is not already in the form y = mx + b), and then plot the corresponding points on the graph. The direction of the inequality symbol will determine whether the line should be solid or dashed, and whether the shaded region should be above or below the line.
The solution to an inequality is the set of all values that make the inequality true. When solving and graphing inequalities simultaneously, you need to find the overlap of the solutions and shaded regions for each individual inequality. The overlapping region will be the solution to the system of inequalities.