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A-CED.1 Warmup M2-002-A07-V03

Create and solve one-variable equations and inequalities, including absolute-value, linear, quadratic, simple rational, and exponential cases.

Create and solve a quadratic inequality from context

Problem

A rectangle has width \(x\) units and length \(x+4\) units, where \(x>0\), and its area is less than \(12~\text{square}~\text{units}\). Use the displayed graph to write and solve the quadratic area inequality, then report every allowable width in the contextual domain.

A scaled graph of A of x equals x squared plus four x for x from negative seven through three. The area target twelve and positive-width domain are shown, but the boundary roots and allowable-width interval are not annotated.
The expanded area model, target 12, and positive-width domain are shown without labeled boundary roots.
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Four variants of this problem type
Curriculum context
Course
Math II
Standard
A-CED.1
Category
Algebra
Domain
Creating Equations
Objective
Create and solve one-variable equations and inequalities, including absolute-value, linear, quadratic, simple rational, and exponential cases.
Problem type
Create and solve a quadratic inequality from context