Math Problem Statement
Solve the system of inequalities: 57 - 7x > 3x - 2 and 22x - 1 < 2x + 47.
Solution
The image contains a system of two inequalities:
Let's solve each inequality step by step.
Inequality 1:
-
First, add to both sides:
-
Then, add to both sides:
-
Divide both sides by :
Inequality 2:
-
Subtract from both sides:
-
Add to both sides:
-
Divide both sides by :
Solution:
Now, combining the results:
- From the first inequality,
- From the second inequality,
The stricter condition is .
Thus, the solution to the system of inequalities is:
Would you like more details or have any questions about this solution?
Related Questions:
- How can we solve similar inequalities with more variables?
- What happens if one inequality had a different direction, e.g., instead of ?
- How would the solution change if the coefficients were fractions?
- Can we graph these inequalities to visualize the solution set?
- How do inequalities relate to systems of equations?
Tip: Always check if the variable's solution in inequalities satisfies both conditions by plugging it back into the original inequalities.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Inequalities
Formulas
Basic inequality rules
Simplifying linear expressions
Theorems
Properties of inequalities
Addition and subtraction properties of inequalities
Suitable Grade Level
Grades 7-9