Math Problem Statement

User uploaded images with algebraic equations for solving.

Solution

I see you've uploaded several images containing mathematical problems. Let's work through them one by one.

From the first image:

  1. Equation 17: 0.315b=2.5b+520.3 - \frac{1}{5}b = 2.5b + \frac{5}{2}
  2. Equation 18: 0.2(3a+12)=0.3(a34)0.2(3a + \frac{1}{2}) = 0.3\left(a - \frac{3}{4}\right)
  3. Equation 19: 12(5z3)=0.25(3z+2)\frac{1}{2}(5z - 3) = 0.25(3z + 2)
  4. Equation 20: 0.7x+34=2.1+x50.7x + \frac{3}{4} = 2.1 + \frac{x}{5}

Would you like me to solve all of these equations? Let me know if you'd prefer me to start with specific ones or focus on detailed explanations for each.

Also, here are some questions to expand the scope:

  1. What methods are typically used to solve linear equations with fractions?
  2. How can you verify the solution of a linear equation?
  3. What is the significance of distributing terms when solving equations?
  4. Why is it important to eliminate fractions in equations?
  5. How does changing the variable's coefficient affect the solution?

Tip: Always aim to clear fractions early in an equation by multiplying by the least common denominator (LCD) to simplify calculations.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Fractions
Variables
Distributive Property

Formulas

ax + b = c
x/a + b = c
ax + by = c

Theorems

Properties of Equality

Suitable Grade Level

Middle to High School