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:

  1. 577x>3x257 - 7x > 3x - 2
  2. 22x1<2x+4722x - 1 < 2x + 47

Let's solve each inequality step by step.


Inequality 1: 577x>3x257 - 7x > 3x - 2

  1. First, add 7x7x to both sides: 57>10x257 > 10x - 2

  2. Then, add 22 to both sides: 59>10x59 > 10x

  3. Divide both sides by 1010: x<5.9x < 5.9


Inequality 2: 22x1<2x+4722x - 1 < 2x + 47

  1. Subtract 2x2x from both sides: 20x1<4720x - 1 < 47

  2. Add 11 to both sides: 20x<4820x < 48

  3. Divide both sides by 2020: x<2.4x < 2.4


Solution:

Now, combining the results:

  1. From the first inequality, x<5.9x < 5.9
  2. From the second inequality, x<2.4x < 2.4

The stricter condition is x<2.4x < 2.4.

Thus, the solution to the system of inequalities is: x<2.4x < 2.4


Would you like more details or have any questions about this solution?

Related Questions:

  1. How can we solve similar inequalities with more variables?
  2. What happens if one inequality had a different direction, e.g., \geq instead of >>?
  3. How would the solution change if the coefficients were fractions?
  4. Can we graph these inequalities to visualize the solution set?
  5. 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