Math Problem Statement
Solve the inequality
Solution
The inequality in the image is:
Step-by-step solution:
Step 1: Simplify both sides
First, simplify the right-hand side: So, the inequality becomes:
Step 2: Eliminate fractions by finding a common denominator
The least common denominator between , 6, and 2 is 12. Multiply every term by 12 to eliminate the fractions: This simplifies to:
Simplifying both sides:
Step 3: Isolate the variable
Move all terms involving to one side and constants to the other:
Step 4: Solve for
Divide both sides by 7:
Final Solution:
The solution to the inequality is:
Would you like further details or have any questions?
Here are 5 related questions for further exploration:
- How would the inequality change if the signs of the fractions were reversed?
- What happens if the coefficient of on one side is negative?
- Can you graph the solution on a number line?
- How would the solution change if the inequality was instead of ?
- What happens if there are no fractions involved?
Tip: Always be careful when multiplying or dividing an inequality by a negative number, as this will reverse the inequality sign.
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Math Problem Analysis
Mathematical Concepts
Algebra
Inequalities
Linear Equations
Formulas
Fraction simplification
Inequality solving
Variable isolation
Theorems
Properties of inequalities
Multiplication of inequalities by negative numbers
Suitable Grade Level
Grades 9-11