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 nn.

We are given the inequality: 3<n4-3 < n \leq 4 Since nn is an integer, the smallest integer that satisfies this inequality is 2-2.

Answer: n=2n = -2


b) What is the inequality shown on the number line?

On the number line:

  • The shaded dot at 4-4 indicates that x=4x = -4 is included.
  • The open circle at 55 indicates that x=5x = 5 is excluded.
  • The line is drawn between 4-4 and 55.

This represents the inequality: 4x<5-4 \leq x < 5

Answer: 4x<5-4 \leq x < 5


c) Solve 23q1>9\frac{2}{3}q - 1 > 9

To solve this inequality:

  1. Add 1 to both sides: 23q>10\frac{2}{3}q > 10
  2. Multiply both sides by 32\frac{3}{2}: q>15q > 15

Answer: q>15q > 15


Would you like further clarification or details on any of these parts?

Here are 5 related questions to practice:

  1. Solve the inequality 2n<6-2 \leq n < 6, where nn is an integer.
  2. What is the inequality represented by a number line with a closed circle at 11 and an open circle at 66?
  3. Solve the inequality 34x+28\frac{3}{4}x + 2 \leq 8.
  4. If 5<x2-5 < x \leq 2, list all integer values of xx.
  5. Represent the inequality 2<y4-2 < y \leq 4 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