Formula Sheet: Linear Inequalities
This chapter explores linear inequalities in one and two variables, explaining their significance in various real-world applications.
Linear Inequalities – Formula & Equation Sheet
Essential formulas and equations from Mathematics, tailored for Class 11 in Mathematics.
This one-pager compiles key formulas and equations from the Linear Inequalities chapter of Mathematics. Ideal for exam prep, quick reference, and solving time-bound numerical problems accurately.
Formula sheet
Key concepts & formulas
Essential formulas, key terms, and important concepts for quick reference and revision.
Formulas
ax + b < 0
Here, a and b are constants. This represents a linear inequality. The solutions are the values of x where the linear expression is less than zero.
ax + b > 0
This shows the conditions under which the linear expression is greater than zero. The solutions indicate where the expression takes positive values.
ax + b ≤ 0
Indicates where the linear expression is less than or equal to zero. Useful for identifying boundary conditions in problems.
ax + b ≥ 0
Defines where the linear expression is greater than or equal to zero, setting constraints for feasible solutions.
ax + by < c
Involves two variables x and y. Represents the region below the line ax + by = c in the Cartesian plane.
ax + by > c
Defines the area above the line ax + by = c. Essential for understanding feasible regions in linear programming.
ax + by ≤ c
Indicates the set of points on or below the line formed by the equation ax + by = c.
ax + by ≥ c
Describes the area on or above the line ax + by = c, establishing constraints for solution sets.
3 < x < 5
A double inequality that states x is greater than 3 and less than 5. This can be used to find a range of acceptable values.
E = mc² (Energy-Mass Equivalence)
In physics, the formula states that energy (E) is equal to mass (m) times the speed of light (c) squared. This underscores the relationship between mass and energy.
Equations
x = a + b
Here, a and b are constants. This is a simple linear equation in one variable. The solution is the value of x.
y = mx + c
The slope-intercept form of a linear equation, where m is the slope, and c is the y-intercept. This is fundamental in graphing linear equations.
ax + b = 0
Represents a linear equation where the solution x = -b/a, demonstrating the balance point of the equation.
2x + 3 = 5
A simple linear equation that shows how to find the value of x. Here, solving leads to x = 1.
5x - 2 = 8
Here x can be solved by rearranging, resulting in x = 2. This showcases the basic technique for linear equations.
3(x - 2) = 12
This represents a linear equation in expanded form. The equation magnifies the importance of order of operations.
y - 5 = k(x - a)
This is the point-slope form of a linear equation, useful for writing equations of a line given a point and slope.
-7 < x ≤ 2
An inequality that indicates the values x can take are greater than -7 and less than or equal to 2.
4x + 7y = 28
This linear equation in two variables describes a straight line on the Cartesian plane, where combinations of x and y satisfy the equation.
x - y = 3
Another form of a linear equation, indicating a line in the Cartesian plane where the difference between x and y is 3.
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