Represent constraints by equations or inequalities and by systems of equations and/or inequalities and interpret solutions as viable or non-viable options in a modeling context.

Sample Practice Questions (3)

A technician is monitoring the temperature of a chemical reaction. The temperature,

T

, must remain between 15 degrees Celsius and 45 degrees Celsius, inclusive. Which inequality represents the non-viable temperatures for this reaction?

15 \leq T \leq 45

T < 15

T > 45

T \leq 15

T \geq 45

15 < T < 45

Multiple choice · diagramSee Answer + Explanation →

A landscape architect is designing a rectangular garden. The length,

L

, must be at least 10 feet, and the width,

W

, must be at least 5 feet. The perimeter of the garden cannot exceed 60 feet. Which system of inequalities represents these constraints?

L \geq 10, W \geq 5, 2 L + 2 W \leq 60

L > 10, W > 5, L + W \leq 60

L \geq 10, W \geq 5, L W \leq 60

L \leq 10, W \leq 5, 2 L + 2 W \leq 60

Multiple choice · diagramSee Answer + Explanation →

Look at the graph below. Which system of inequalities describes the shaded region?

y \leq 2

and

x > 1

y \geq 2

and

x < 1

y < 2

and

x \leq 1

y \leq 2

and

x \geq 1

Multiple choice · diagramSee Answer + Explanation →

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More Algebra I Standards

NY-A.SSE.1aInterpret parts of an expression such as terms factors and coefficients in context.→NY-A.SSE.1bInterpret complicated expressions by viewing one or more of their parts as a single entity.→NY-A.SSE.2Use the structure of an expression to identify ways to rewrite it. For example see x⁴ - y⁴ as (x²)² - (y²)² and factor accordingly.→NY-A.SSE.3aFactor a quadratic expression to reveal the zeros of the function it defines.→

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