Math Problem Statement
Solve for x :
7x−2(x−4)>−2x+1
Solution
Let's solve the inequality step by step:
The inequality is:
Step 1: Distribute the on the left side
Distribute to both terms inside the parentheses:
This simplifies to:
Step 2: Combine like terms
Now combine the terms involving on the left side:
Step 3: Move the -terms to one side
To eliminate from the right side, add to both sides:
This simplifies to:
Step 4: Move the constant term to the other side
Subtract 8 from both sides:
Step 5: Solve for
Now divide both sides by 7:
Final Answer:
The solution to the inequality is:
Would you like any further explanation on this solution? Or have any additional questions?
Here are some follow-up questions to explore:
- How do you handle inequalities involving absolute values?
- What happens if both sides of an inequality are multiplied by a negative number?
- How can we graph the solution on a number line?
- What are the key differences between solving an equation and solving an inequality?
- What if the inequality was ? How would that change the solution?
Tip: Always pay attention when multiplying or dividing by negative numbers in inequalities; it flips the inequality sign!
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Math Problem Analysis
Mathematical Concepts
Algebra
Inequalities
Linear Equations
Formulas
Distributive Property
Solving linear inequalities
Theorems
Basic rules for solving inequalities
Suitable Grade Level
Grades 7-9