Math Problem Statement

Module 7-5 Extended Practice - Systems of Inequalities.pdf

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Solution

The uploaded file contains a series of systems of inequalities that need to be solved by graphing and shading the solution sets. Below are the problems listed in the document:

  1. y<6y < 6, y1y \geq 1 y>x+3y > x + 3, y2x5y \leq 2x - 5

  2. y1y \leq 1, 2x12x - 1 y<1y < -1, 3x63x - 6 y1y \leq 1, 2x52x - 5

  3. y4y \geq -4, 3x13x - 1 y<2x3y < 2x - 3, x<3x < 3 y3x+2y \geq -3x + 2

  4. 5x+2y<165x + 2y < -16, 3x+y<13x + y < -1 3x+4y43x + 4y \leq -4, x2y>12x - 2y > -12

  5. y<1y < 1, 2x+22x + 2 3x+4y>283x + 4y > 28, x1x \geq 1 2x12x - 1, x2y4x - 2y \geq -4

  6. 3x+4y283x + 4y \geq -28, x2y>4x - 2y > 4 x4y<12x - 4y < 12, 3xy73x - y \leq 7

You need to graph each system and shade the solution set, which is the region where all inequalities are satisfied simultaneously.

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Math Problem Analysis

Mathematical Concepts

Systems of Inequalities
Graphing Inequalities
Linear Inequalities

Formulas

y < 6
y ≥ 1
y > x + 3
y ≤ 2x - 5
y ≤ 1
2x - 1
y < -1
3x - 6
y ≥ -4
3x - 1
y < 2x - 3
x < 3
y ≥ -3x + 2
5x + 2y < -16
3x + y < -1
3x + 4y ≤ -4
x - 2y > -12
3x + 4y ≥ -28
x - 2y > 4
x - 4y < 12
3x - y ≤ 7

Theorems

Graphing linear inequalities
Shading solution sets of inequalities

Suitable Grade Level

Grades 9-11