more structure work common core algebra 1 homework answer key

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Math - More structure work in lesson 1-9

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Name: ____________________________________ date: __________________, common core algebra i, unit #1 – the building blocks of algebra – lesson, m ore s tructure work, common core algebra i, the more you are able to see structure in the various expressions that you deal with, the easier it will be to, manipulate complex expressions. we will work with structure throughout the course. we can now look at, some larger structural issues that include equivalency., exercise #1: consider the somewhat complex expression x x  4   2  x 4 ., which type of equivalent expression we might need would depend on the context of what we were trying to do, with the math. for now, we want to get practice with writing various expressions in an equivalent form, and, being able to test that equivalency., exercise #2: consider the expression  x  4  x  5    x  4  x 2 . write an equivalent expression that is in, the form of the product of two binomials. test the equivalency with a value of x. show your test., exercise #3: which of the following is equivalent to the expression  x  3  2 x  7    x  3  x 4  show the, manipulations that lead to your choice., (1)  x  3  x 3  (3)  x  6  x 10 , (2)  x  3  x 11  (4)  x  6  x 4 , (a) write an equivalent trinomial expression. test, the equivalency with a value of x  1. show the, (b) write an equivalent expression that is in the, form of a product of two binomials. also test, the equivalency with x  1., strangely enough, this type of manipulation, where there is a common binomial multiplying two other terms, is, frequent enough that it is also a good skill to become fluent in. get some additional practice in the next, exercise. be careful when subtraction is involved (see the last exercise)., exercise #4: rewrite each of the following expressions as an equivalent product of two binomials., (a) x x  5   7  x 5  (b) 3 x x  2   4  x 2  (c)  2 x x  4  x 4, (d)  x  6  x  3    x  9  x 3  (e)  2 x  1  x  4    x  6  x 4 , remember, that we want to always look for mindful manipulations in order to help us solve our problems., sometimes we won’t know whether those manipulations will pay dividends, but as long as we know we are, making manipulations that retain equivalency then they are worth a try., exercise #5: the binomial 4 n  1 is equal to 7 for some value of n. what is the value of the expression shown, below for the same value of n. do not solve for n in this problem. use mindful manipulations and look for, structure to help solve this problem.,  3 n  1  4 n  1    n  2  4 n 1 , applications, 4. when figuring out the amount of mulch would be needed for alex’s back yard, he created an equation that, approximates the number of bags, b, he’ll use. if his equation is b  4 2 x  7   3 2 x 7 and  2 x  7  is, equal to 2, how many bags will he need show your mindful manipulations., 5. alex’s friend pablo comes up with an exact equation to find out how many bags he needs. use his equation, to find out how many bags will actually be needed if b = x  2 x  7   3 2 x  7    x  4   2 x  7 , where the, quantity  2 x  7  equals 4. show how you arrive at your answer., 6. in most of the previous examples there were only two terms. extend your work with using the distributive, law “backwards” and write the following as a product of binomials., (a) x x  2   3  x  2   4 x x  2  (b) 2 x x  5   3  x  5    x  1   x  5 , 7. write x x  2   3 2  x as a product of binomials. hint: you may want to manipulate  2  x first. check to, see if you have written an equivalent expression by testing x  5..

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Topic : Expressions and Operations

Subject : algebra 1.

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Common Core Algebra I Math (Worksheets, Homework, Lesson Plans)

Related Topics: Common Core Math Resources, Lesson Plans & Worksheets for all grades Common Core Math Video Lessons, Math Worksheets and Games for Algebra Common Core Math Video Lessons, Math Worksheets and Games for all grades

Looking for video lessons that will help you in your Common Core Algebra I math classwork or homework? Looking for Common Core Math Worksheets and Lesson Plans that will help you prepare lessons for Algebra I students?

The following lesson plans and worksheets are from the New York State Education Department Common Core-aligned educational resources. Eureka/EngageNY Math Algebra I Worksheets.

These Lesson Plans and Worksheets are divided into five modules.

Algebra I Homework, Lesson Plans and Worksheets

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