Solving Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (>, <, ≥, ≤).

Front

How do you solve a linear inequality?

Back

To solve a linear inequality, isolate the variable on one side of the inequality sign using inverse operations, similar to solving an equation.

Front

What happens to the inequality sign when you multiply or divide by a negative number?

Back

When you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality sign.

Front

Solve: 3(x-2) < 2(x+9)

Back

x < 24

Front

Solve: 6x + 10 > 5x - 12

Back

x > -22

Front

Solve: 7(x + 3) < 5x + 13

Back

x < -4

Front

Solve: 5(v + 3) - 10v > -10

Back

v < 5

Front

Solve: -8b - 8 > 56

Back

b < -8

Front

What is the difference between strict and non-strict inequalities?

Back

Strict inequalities (<, >) do not include the boundary value, while non-strict inequalities (≤, ≥) do include the boundary value.

Front

What is the graphical representation of a linear inequality?

Back

The graphical representation of a linear inequality is a shaded region on one side of a boundary line, which represents all the solutions to the inequality.