Math Problem Statement
Solution
The equation from the image is:
Let's solve it step by step:
- Combine like terms. The terms involving are and . To combine them, we need a common denominator. The least common denominator between 9 and 3 is 9. So, rewrite as .
Now the equation looks like:
-
Combine the -terms: Now the equation becomes:
-
Add 1 to both sides to move the constant term to the right side:
-
To solve for , multiply both sides by the reciprocal of , which is :
-
Simplify:
So, the solution is:
Would you like further details or have any questions? Here are some related questions:
- How do you find the least common denominator when combining fractions?
- Why is it important to combine like terms in an equation?
- How do you solve equations that involve fractions and constants?
- What happens if you multiply both sides of an equation by the reciprocal of a fraction?
- How can checking your solution help ensure accuracy in solving equations?
Tip: When solving equations with fractions, it's often helpful to clear the denominators by multiplying through by the least common denominator!
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Algebra
Equations with Fractions
Combining Like Terms
Solving Linear Equations
Formulas
ax + b = c
Common Denominator Method for Combining Fractions
Theorems
Properties of Equality
Solving Linear Equations with Fractions
Suitable Grade Level
Grades 8-10
Related Recommendation
Solving a Linear Equation with Fractions: (4/5)x - (1/3)x = 7
Solve Linear Equation with Fractions: (3(5/9)x + 4/27)/2 = 3
Solving Linear Equations Involving Fractions: (4x/9) + (2x/3) = (5/7) - (7/6)
Solving a Linear Equation Involving Fractions: 7/3x - 1/6 = 5/9x - 2/3
Solve Fractional Algebra Equation: Step-by-Step Solution