Math Problem Statement
Solve the following:
a) Write down the smallest possible value of n where -3 < n ≤ 4, and n is an integer.
b) What is the inequality shown on the number line between -4 and 5, with a closed circle at -4 and an open circle at 5?
c) Solve 2/3q - 1 > 9.
Solution
Let's analyze and solve the three parts of the question from the image you provided:
a) Write down the smallest possible value of .
We are given the inequality: Since is an integer, the smallest integer that satisfies this inequality is .
Answer:
b) What is the inequality shown on the number line?
On the number line:
- The shaded dot at indicates that is included.
- The open circle at indicates that is excluded.
- The line is drawn between and .
This represents the inequality:
Answer:
c) Solve
To solve this inequality:
- Add 1 to both sides:
- Multiply both sides by :
Answer:
Would you like further clarification or details on any of these parts?
Here are 5 related questions to practice:
- Solve the inequality , where is an integer.
- What is the inequality represented by a number line with a closed circle at and an open circle at ?
- Solve the inequality .
- If , list all integer values of .
- Represent the inequality on a number line.
Tip: When solving inequalities involving fractions, multiplying both sides by the reciprocal can simplify the process.
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Math Problem Analysis
Mathematical Concepts
Inequalities
Number Line
Solving Linear Inequalities
Formulas
Solving linear inequalities
Number line representation
Theorems
Properties of inequalities
Basic algebraic manipulation
Suitable Grade Level
Grades 6-8