Is there more than one way Can you get x alone? solution?helpmeteach.weebly.com/uploads/1/7/1/0/17102056/_im_8__ch_3.2.… · Is there more than one way to solve? Can you get x alone?

IM 8 Ch 3.2.5 How Can I Solve Complicated Equations

CPM Materials modified by Mr. Deyo

How can you simplify?

Is there more than one way to solve?

Can you get x alone?

How can you check your solution?

Common Core Standard: 8.EE.7b


By the end of the period, I will apply the Distribuve Property to solve linear equaons.

I will demonstrate this by compleng Four‐Square notes and by solving problems in a pair/group acvity.

Learning TargetTitle: IM8 ‐ Ch. 3.2.5 How Can I Solve Complicated Equaons? Date:


Home Work: Sec. 3.2.5Desc. Date Due

Review & Preview

2 Problems: 3‐114, 3‐117



Vocabulary1) Distributive Property

2) Additive Inverse

3) Multiplicative Inverse

4) Order of Operations



3.2.5 How Can I Solve Complicated Equations?Not all equations are as simple as the equations you have solved so far. However, many equations that look complicated just need to be broken into simpler, familiar parts. In this lesson, you will use algebra tiles to work with situations that combine addition and multiplication. Then you will solve equations that contain complicated parts.While solving equations in this lesson, keep these focus questions in mind:

How can you simplify?

Is there more than one way to solve?

Can you get x alone?

How can you check your solution?


3107 So far in this course, you have solved singlevariable equations like: 3x + 7 = −x − 3. Consider this change to that equation:

3(x + 7) = −x − 3. What is different about the equations? How will the changes made to the original equation change the steps needed to solve the equation?

3x + 7 = x 3 3(x + 7) = x 3


1

xy

y

yx

x

y2

y2

x2

xy

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x2

3108a Use algebra tiles to build, draw, and simplify the expression.Simplified Expression:

Original Expression: 3(x + 4)


1

xy

y

yx

x

y2

y2

x2

xy

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x2

3108b Use algebra tiles to build, draw, and simplify the expression.Simplified Expression:

Original Expression: 4(2x − 1)


1

xy

y

yx

x

y2

y2

x2

xy

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x2

3108c Use algebra tiles to build, draw, and simplify the expression.Simplified Expression:

Original Expression: 2(x + 5) + 3


1

xy

y

yx

x

y2

y2

x2

xy

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x2

3108d Use algebra tiles to build, draw, and simplify the expression.Simplified Expression:

Original Expression: 3(x − 2) + 5


3109 In a previous class, you used the Distributive Property to rewrite problems with parentheses similar to the ones above. Use the Distributive Property to complete and simplify each expression below. Read the Math Notes box at the bottom of the page if you need help getting started.

The Distributive Property The Distributive Property states that for any three terms a, b, and c:

a(b + c) = ab + acThat is, when a multiplies a group of terms, such as (b + c), it multiplies each term of the group. For example, when multiplying 2(x + 4), the 2 multiplies both the x and the 4. This can be represented with algebra tiles, as shown below.

2(x + 5) = 2 · x + 2 · 5 = 2x + ______ 3(2x + 1) = 3 · 2x + 3 · __ = ______

−2(x + 3) = −2 · __ + −2 · __ = ____ −3(2x − 5) = ________ = _________


3110

Explanation

• Combine Like Terms• Add/Subtract ___ to Both Sides• Divide Both Sides by ___• Distributive Property

Now use what you learned in the previous three problems to solve for x. Show your steps and check your answer. You may want to use algebra tiles and an Equation Mat to help you visualize the equation.

3(x + 7) = x 3


3111a

Explanation

• Distributive Property• Combine Like Terms• Additive Inverse• Multiplicative InverseSolve for the variable. Record

your work & check the solution.

3x − 2(5x + 3) = 14 − 2x


3111b

Explanation



3(x + 1) − 8 = 14 − 2(3x − 4)


Earlier in this course, you learned that −(x − 3) was the same as −x + 3, because (x − 3) in the “−” region could be “flipped” to −x + 3 in the “+” region, as shown below.

3112

Use what you have learned in this lesson to explain algebraically why “flipping” works. That is, why does −(x − 3) = −x + 3?


3113a

Explanation



3(5x + 2) = 8x + 20

http://homework.cpm.org/cpmhomework/homework/category/CC/textbook/CC3/chapter/Ch3/lesson/3.2.5/problem/3113

http://homework.cpm.org/cpm-homework/homework/category/CC/textbook/CC3/chapter/Ch3/lesson/3.2.5/problem/3-113


3113b

Explanation



−2(x − 3) + 4x = −(−x + 1)




a)

c)

3114 Simplify each algebraic expression.

b)

d)

x + 3x − 3 + 2x2 + 8x − 5 3y + 14y2 − 6y2 − 9y + 1 − y − 3y

2y2 + 30xy − 2y2 + 4y − 4x x − 0.2x




3115Louis recorded how many times he could jump rope without stopping. Here is his data:

http://www.cpm.org/technology/general/stats/ http://homework.cpm.org/cpmhomework/homework/category/CC/textbook/CC3/chapter/Ch3/lesson/3.2.5/problem/3115

50 15 102 64 29 55 100 97 48 81 61

Find the median, upper quartile, and lower quartile of his data.

Median:

Upper Quartile:

Lower Quartile:

http://www.cpm.org/technology/general/stats/



3116Find the area and perimeter of the shape. Show your work.

Area Perimeter


Area of a rectangle = base x height

Perimeter of a rectangle = 2(base + height) Circumference = 2 r



This problem is a checkpoint for unit rates and proportions. It will be referred to as Checkpoint 3. In parts (a) through (c), use the given information to find the unit rate. In parts (d) through (f), write and solve a proportion based on the given information.

3117a,b,c

b) What is the weight per cm?

a) If 2.25 pounds of bananas cost $1.89, what is the cost per pound?

c) Use the graph below to find the refill cost per bottle.




This problem is a checkpoint for unit rates and proportions. It will be referred to as Checkpoint 3. In parts (a) through (c), use the given information to find the unit rate. In parts (d) through (f), write and solve a proportion based on the given information.

3117d,e,f

e) If a basketball player made 72 out of 85 freethrow attempts, how many could she expect to make in 200 attempts?

d) If 200 vitamins cost $4.75, what should 500 vitamins cost? f) A cookie recipe uses

teaspoon of vanilla with cup of flour. How much vanilla should be used with five cups of flour?


If you needed help solving these problems correctly, then you need more practice. Review the Checkpoint 3 materials and try the practice problems. Also, consider getting help outside of class time. From this point on, you will be expected to do problems like these quickly and easily.


Documents

Is there more than one way Can you get x alone? solution?helpmeteach.weebly.com/uploads/1/7/1/0/17102056/_im_8__ch_3.2.… · Is there more than one way to solve? Can you get x alone?