Math Problem Statement

Is the ordered pair (5, 0) a solution to the inequality 4x - 7y > 4. Why or why not?

(A) Yes, 20 > 4

(B) Yes, 27 > 4

(C) No, -7 < 4

(D) No, -35 < 4

Solution

To determine if the ordered pair (5,0)(5, 0) is a solution to the inequality 4x7y>44x - 7y > 4, we substitute x=5x = 5 and y=0y = 0 into the inequality and see if it holds true.

  1. Substitute x=5x = 5 and y=0y = 0 into 4x7y>44x - 7y > 4: 4(5)7(0)>44(5) - 7(0) > 4

  2. Simplify the expression: 200>420 - 0 > 4 20>420 > 4

This inequality is true. Therefore, (5,0)(5, 0) is indeed a solution to the inequality 4x7y>44x - 7y > 4.

Answer:

The correct choice is (A) Yes, 20 > 4.

Would you like further details or have any questions?


Here are some related questions to expand on this concept:

  1. How would you determine if an ordered pair is a solution for a different inequality, like 3x+2y63x + 2y \leq 6?
  2. What is the process for checking if a point lies on the boundary of an inequality solution region?
  3. Can a point satisfy an inequality but not its corresponding equation?
  4. How do we graphically represent the solution set of an inequality on a coordinate plane?
  5. What changes in the inequality 4x7y44x - 7y \geq 4 compared to 4x7y>44x - 7y > 4?

Tip: Always check your substitution carefully when determining if a point is a solution to an inequality or equation.

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Math Problem Analysis

Mathematical Concepts

Algebra
Inequalities
Ordered Pairs

Formulas

Inequality expression substitution: 4x - 7y > 4

Theorems

Substitution Method for Solving Inequalities

Suitable Grade Level

Grades 7-9