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Creating and Solving Quadratic Equations in One Variable

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Lesson Plans and Worksheets for Algebra I
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Common Core For Algebra I

Examples, solutions, and videos to help Algebra I students learn how to interpret word problems to create equations in one-variable and solve them (i.e., determine the solution set) using factoring and the zero product property.

New York State Common Core Math Algebra I, Module 4, Lesson 7

Worksheets for Algebra 1

Lesson 7 Summary

When provided with a verbal description of a problem, represent the scenario algebraically. Start by identifying the unknown quantities in the problem and assigning variables. For example, write expressions that represent the length and width of an object.

Solve the equation using techniques previously learned, such as factoring and using the zero product property. The final answer should be clearly stated and be reasonable in terms of the context of the problem.

Lesson 7 Examples

Example 1

The length of a rectangle is 5 in. more than twice a number. The width is 4 in. less than the same number. If the area of the rectangle is15 in2, find the unknown number.

Example 2

A picture has a height that is 4/3 its width. It is to be enlarged so that the ratio of height to width remains the same but the area is 192 sq. in. What are the dimensions of the enlargement?

Example 3

One base of a trapezoid is three times the length of the second base. The height of the trapezoid is 2 in. smaller than the second base. If the area of the trapezoid is 30 in2, find the lengths of the bases and the height of the trapezoid.

Example 4:

A garden measuring 12 m by 16 m is to have a pedestrian pathway that is w meters wide installed all the way around it, increasing the total area to 285 sq. m. What is the width, w, of the pathway?

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