Math Problem Statement
1.1 Given the following linear inequality: − 6 < 2𝑥 − 4 ≤ 2 1.1.1 Solve the linear inequality. (2) 1.1.2 Represent your solution on a number line. (1)
Solution
1.1.1 Solve the linear inequality:
Given the inequality:
Step 1: Solve the first part of the inequality:
Add 4 to both sides:
Now, divide both sides by 2:
So, the first part simplifies to:
Step 2: Solve the second part of the inequality:
Add 4 to both sides:
Now, divide both sides by 2:
Step 3: Combine both parts: So the solution is:
1.1.2 Represent your solution on a number line:
The solution is represented as:
- An open circle at (because cannot equal ),
- A filled circle at (because can equal ),
- A shaded region between and to indicate all values of in this range.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Inequalities
Number Line Representation
Formulas
Solving compound inequalities
Properties of inequalities
Theorems
Addition and multiplication properties of inequalities
Suitable Grade Level
Grades 8-10