Math Problem Statement

The original question submitted by the user involves arithmetic operations, inequalities, and solving basic algebraic equations.

Solution

Let's go through the questions visible in the image:

Section 1:

This section seems to be about inequalities. The inequalities appear to be in the following format:

  1. 3,1-3,1
  2. 6,7-6,7
  3. 4,5,24, -5, -2

These might involve ordering or solving. However, the exact nature is unclear without more information.

Section 2:

Basic arithmetic and operations with negative numbers:

  1. 6+(4)=?6 + (-4) = ?
    • Solution: 6+(4)=26 + (-4) = 2
  2. (1)+(9)=?(-1) + (-9) = ?
    • Solution: (1)+(9)=10(-1) + (-9) = -10
  3. (78)(8)=?\left( -\frac{7}{8} \right) - (-8) = ?
    • Solution: 78+8=578-\frac{7}{8} + 8 = \frac{57}{8}
  4. 28=?\frac{-2}{8} = ?
    • Solution: 28=14\frac{-2}{8} = -\frac{1}{4}

Section 3: Calculations

  1. 92×(3)=?9 - 2 \times (-3) = ?
    • Solution: 92×(3)=9+6=159 - 2 \times (-3) = 9 + 6 = 15
  2. 2×(59)=?-2 \times (-5 - 9) = ?
    • Solution: 2×(14)=28-2 \times (-14) = 28
  3. 30:(3)2=?30 : (-3)^2 = ?
    • Solution: 30:9=309=10330 : 9 = \frac{30}{9} = \frac{10}{3}
  4. 8×(1+76)=?8 \times \left( -1 + \frac{7}{6} \right) = ?
    • Solution: 8×16=86=438 \times \frac{1}{6} = \frac{8}{6} = \frac{4}{3}

Would you like more detailed explanations on any part of the problems, or additional steps for better understanding?

Relative Questions:

  1. How do you simplify expressions involving negative numbers and fractions?
  2. What is the general approach to solving inequalities?
  3. How does multiplying and dividing by negative numbers affect inequality signs?
  4. What is the order of operations when dealing with nested parentheses and powers?
  5. Can you explain how to handle subtraction of negative numbers?

Tip: Always solve operations inside parentheses first and keep an eye on the signs, especially with negative numbers.

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Math Problem Analysis

Mathematical Concepts

Inequalities
Basic Arithmetic
Negative Numbers
Fractions
Multiplication and Division
Order of Operations

Formulas

Addition and subtraction of negative numbers: a + (-b) = a - b
Multiplication and division of negative numbers: a × (-b) = -ab, (-a) ÷ b = -a/b
Simplifying fractions: a/b

Theorems

Distributive Property
Multiplication and Division Rules for Negative Numbers
Order of Operations (PEMDAS)

Suitable Grade Level

Grade 7-9