Math Problem Statement
Solve multi-step equations with fractions as shown in the image.
Solution
Let's solve the multi-step equations with fractions from the image.
a)
- First, simplify the terms inside the parentheses: So the equation becomes:
- Simplify : Now the equation is:
- Subtract from both sides:
- Solve for :
b)
- Distribute over : So the equation becomes:
- To eliminate the fractions, multiply the entire equation by 9:
- Subtract 30 from both sides:
- Solve for :
c)
- First, simplify the terms inside the parentheses: So the equation becomes:
- Multiply both sides by 5 to eliminate the :
- Multiply both sides by 4 to eliminate the denominator:
- Subtract 3 from both sides:
- Solve for :
d)
- Multiply the entire equation by 10 to eliminate the fractions:
- Distribute the terms: Simplify:
- Subtract 5 from both sides:
- Solve for :
Would you like further explanations on any step? Here are some related questions for practice:
- How would you simplify equations that have variables on both sides?
- What is the process of eliminating fractions in multi-step equations?
- How can you check your solution for fractional equations?
- How do you factor equations that involve fractions?
- How would you approach solving an equation if all terms are fractions?
Tip: Always try to eliminate fractions early by multiplying through by the least common denominator.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Fractions
Multi-Step Equations
Formulas
Basic operations with fractions
Solving linear equations
Theorems
Properties of equality
Distributive property
Suitable Grade Level
Grades 8-10