Math Problem Statement

The user uploaded a set of math problems involving solving equations and word problems. It includes tasks like solving for x in equations, solving perimeter problems, and applying formulas for surface area of a cylinder.

Solution

Let’s solve the questions step by step. I'll start with the first question and work through them systematically:


1. x48=3\frac{x}{4} - 8 = -3

Step 1: Add 8 to both sides:
x4=3+8\frac{x}{4} = -3 + 8 x4=5\frac{x}{4} = 5

Step 2: Multiply both sides by 4:
x=54x = 5 \cdot 4 x=20x = 20


2. 14(3x5)=1\frac{1}{4}(3x - 5) = -1

Step 1: Multiply through by 4 to eliminate the fraction:
3x5=43x - 5 = -4

Step 2: Add 5 to both sides:
3x=4+53x = -4 + 5 3x=13x = 1

Step 3: Divide by 3:
x=13x = \frac{1}{3}


Would you like me to continue solving the rest of the questions? Let me know if you’d like me to elaborate further on any step or tackle specific questions. Here's a quick follow-up:

  1. Would you like all questions completed in order?
  2. Do you want just certain problems explained in detail?
  3. Should I clarify a particular step in the solved equations?
  4. Would you like a formula reference for some questions (e.g., problem 12)?
  5. Do you want additional practice problems based on similar concepts?

Tip: Always check your solution by substituting it back into the original equation!

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Word Problems
Algebraic Equations
Surface Area of a Cylinder

Formulas

Perimeter of Rectangle
Surface Area of a Cylinder: SA = 2πr² + 2πrh

Theorems

Linear Equation Solution
Surface Area Formula

Suitable Grade Level

Grades 6-9