priscilla98 said:Homework Statement
1. 9x^2 + 12x + 4 ≥ 0
2. 2 - 5x - 3x^2 ≤ 0
Homework Equations
The Attempt at a Solution
1. Can't you factor this into (3x + 2) (3x + 2)?
2. Looking at this inequality, I am thinking if you can change this inequality into 3x^2 + 5x + 2.
A linear inequality in pre-calculus is an algebraic expression that contains a variable, an inequality symbol (such as <, >, ≤, or ≥), and a constant. It represents a range of values that satisfy the inequality, rather than a single value. For example, 2x + 3 < 10 is a linear inequality.
To graph a linear inequality, first isolate the variable on one side of the inequality symbol. Then, treat the inequality symbol as an equal sign and graph the resulting linear equation. Finally, shade the region above or below the line depending on the inequality symbol. If the symbol is < or >, use a dashed line to represent the boundary of the shaded region. If the symbol is ≤ or ≥, use a solid line.
The solution to a linear inequality is the set of all values that make the inequality true. In other words, it is the range of values that satisfy the inequality. This can be represented on a number line or graphically as a shaded region.
To solve a system of linear inequalities, first graph each inequality individually to determine the shaded regions. Then, find the overlapping region of all the shaded regions. This overlapping region represents the solution to the system of inequalities.
Linear inequalities are used in many real-life situations, such as setting budgets, determining sales goals, and creating production schedules. They can also be used to represent constraints in optimization problems, such as maximizing profit or minimizing cost. In general, linear inequalities are used to represent relationships between variables and determine the range of values that satisfy those relationships.