Math Problem Statement
-2(a - 7) - 3a ≥ -31
Solution
Let's solve the given inequality step by step:
Given Inequality:
Step 1: Distribute into
Thus, the inequality becomes:
Step 2: Combine like terms
So, the inequality is now:
Step 3: Isolate the term with
Subtract 14 from both sides:
Step 4: Solve for
To isolate , divide both sides of the inequality by . Remember: When dividing or multiplying an inequality by a negative number, the inequality sign flips.
Final Solution:
Conclusion:
The solution to the inequality is .
Would you like more details or have any questions on these steps?
Here are 5 related questions to expand your understanding:
- What happens to the inequality symbol when dividing by a negative number?
- How do you check if a value satisfies the inequality?
- How would the solution change if the inequality was instead of ?
- What are the key differences between solving an equation and an inequality?
- Can you graph the solution on a number line?
Tip: When solving inequalities, always remember to reverse the inequality symbol when multiplying or dividing by a negative number!
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Algebra
Inequalities
Formulas
Distributive property
Combining like terms
Theorems
Rules for solving inequalities
Inverse operations
Suitable Grade Level
Grades 7-9