Math Problem Statement
Solve the equation: (1/3)x + 1/5 = -2((5/6)x + 5).
Solution
The equation provided in the image is:
Let's go through the steps to solve it:
Step 1: Distribute the -2 on the right-hand side
So, the equation becomes:
Step 2: Eliminate fractions by multiplying the entire equation by the least common denominator (LCD) of 3 and 5, which is 15.
Multiply every term by 15: This simplifies to:
Step 3: Move all terms involving to one side and constant terms to the other side.
Step 4: Solve for
Simplify the fraction:
Thus, the solution is:
This matches the solution given in the image.
Would you like further details or have any questions?
Here are five related questions:
- How do you simplify a fraction like ?
- What are the steps to clear fractions in an equation?
- How do you solve equations involving the distributive property?
- What is the significance of the least common denominator in equations with fractions?
- How can you check if your solution for is correct?
Tip: Always try to clear fractions early in solving equations for easier simplification!
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Fractions
Distributive Property
Formulas
Linear equation formula: ax + b = cx + d
Distributive Property: a(b + c) = ab + ac
Theorems
Basic algebraic operations
Least Common Denominator (LCD)
Suitable Grade Level
Grades 8-10