Math Problem Statement

For this two-variable inequality, put the number 1 in for x and select the set of matching numbers for y. The inequality is y > x + 3.

Solution

The inequality given in the image is:

y>x+3y > x + 3

We are asked to substitute x=1x = 1 into this inequality and find the set of values for yy that satisfy the inequality.

Step 1: Substitute x=1x = 1 into the inequality.

y>1+3y > 1 + 3

This simplifies to:

y>4y > 4

Step 2: Identify matching values for yy.

The inequality y>4y > 4 means that any value of yy greater than 4 will satisfy the inequality. Therefore, possible values for yy could be:

  • y=5y = 5
  • y=6y = 6
  • y=10y = 10, etc.

In general, yy can be any number greater than 4.

Would you like further details or have any other questions about this problem?

Here are 5 related questions you might consider:

  1. What happens if we change the inequality to yx+3y \geq x + 3?
  2. How would the solution change if xx were a different number, say x=2x = 2?
  3. What is the graphical representation of the inequality y>x+3y > x + 3?
  4. How can we solve similar inequalities involving negative numbers for xx?
  5. What is the solution for yy if the inequality were y<x+3y < x + 3?

Tip: When solving inequalities, always consider the boundary values and whether they are included (for \geq or \leq) or excluded (for >> or <<).

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Math Problem Analysis

Mathematical Concepts

Inequalities
Substitution

Formulas

y > x + 3

Theorems

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Suitable Grade Level

Grades 6-8