Algebra 1, Homework Practice Workbook (MERRILL ALGEBRA 1)
2nd Edition
ISBN: 9780076602919
Author: McGraw-Hill Education
Publisher: McGraw-Hill Education
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Question
Chapter 2.3, Problem 57HP
To determine
Write a paragraph explaining the order of the steps that you would take to solve a multistep equation.
Expert Solution & Answer
Answer to Problem 57HP
Explanation of Solution
Given:
Concept Used:
Solving Multi-Step Equations The word “multi” means more than two, or many. That’s why solving multi-step equations are more involved than one-step and two-step equations because they require more steps.
The main goal in solving multi-step equations, just like in one-step and two-step equations, is to isolate the unknown variable on one side of the equation while keeping the constant or number on the opposite side.
However, there is no rule on where to keep the variable. It all depends on your preference. The “standard” or usual way is to have it on the left side. But there are cases when it makes more sense to keep it on the right side of the equation.
Since we are dealing with equations, we need to keep in mind that whatever operation we perform on one side must also be applied on the other to keep the equation “balanced”.
This concept of performing the same operation in both sides applies to the four arithmetic operations, namely: addition, subtraction, multiplication, and division. For example, if we add 5 on the left side of the equation we must also add 5 on the right side.
Key steps to remember:
1) Get rid of any grouping symbols such as square brackets, parentheses, etc, by applying the Distributive Property of Multiplication over Addition.
2) Simplify both sides of the equation, if possible, by combining like terms.
3) Decide where you want to keep the variable because that will help you decide where to place the constant.
4) Eliminate numbers or variables by applying opposite operations: addition and subtraction are opposite operations as in the case of multiplication and division.
Calculation:
Examples of How to Solve Multi-Step Equations:
Equation:
This is a typical problem in multi-step equations where there are variables on both sides. Notice that there is no parenthesis in this equation and no like terms to combine on both sides of the equation.
Clearly, our first step is to decide where to keep or isolate the unknown variable x .
Since 7x is “larger” than 2x , then we might as well keep it to the left side.
This means we will have to get rid of the 2x on the right side.
To do that, we need to subtract both sides of the equation by 2x because the opposite of + 2x is - 2x .
After doing so, it is nice to see just the variable x on the left side. This implies that we have to move all the constants to the right side by eliminating +3 on the left side. The opposite of ++3 is -3, therefore, we will subtract both sides by 3.
The last step is to isolate the variable x by itself on the left side of the equation.
Since +5 is multiplying x , then its opposite operation is to divide by +5.
So, we are going to divide both sides by 5 and then we are done!
Solution:
| Original Equation | |
| Subtract 2x from both sides | |
| Simplify | |
| Subtract 3 from both sides | |
| Simplify | |
| Divide each side by 5. The coefficient of x | |
| Simplify and final solution. | |
Conclusion: Result:
Get rid of all numbers which are in the sum or difference with x by subtract or add these numbers on each side and then get rid of all number which are in the product or quotient with x by divide or multiply these numbers on each side.
Thus,
Chapter 2 Solutions
Algebra 1, Homework Practice Workbook (MERRILL ALGEBRA 1)
Ch. 2.1 - Prob. 1AGPCh. 2.1 - Prob. 1BGPCh. 2.1 - Prob. 2GPCh. 2.1 - Prob. 3GPCh. 2.1 - Prob. 4AGPCh. 2.1 - Prob. 4BGPCh. 2.1 - Prob. 5GPCh. 2.1 - Prob. 1CYUCh. 2.1 - Prob. 2CYUCh. 2.1 - Prob. 3CYU
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- You are given a plane Π in R3 defined by two vectors, p1 and p2, and a subspace W in R3 spanned by twovectors, w1 and w2. Your task is to project the plane Π onto the subspace W.First, answer the question of what the projection matrix is that projects onto the subspace W and how toapply it to find the desired projection. Second, approach the task in a different way by using the Gram-Schmidtmethod to find an orthonormal basis for subspace W, before then using the resulting basis vectors for theprojection. Last, compare the results obtained from both methodsarrow_forwardPlane II is spanned by the vectors: - (2) · P² - (4) P1=2 P21 3 Subspace W is spanned by the vectors: 2 W1 - (9) · 1 W2 1 = (³)arrow_forwardshow that v3 = (−√3, −3, 3)⊤ is an eigenvector of M3 . Also here find the correspondingeigenvalue λ3 . Just from looking at M3 and its components, can you say something about the remaining twoeigenvalues? If so, what would you say? find v42 so that v4 = ( 2/5, v42, 1)⊤ is an eigenvector of M4 with corresp. eigenvalue λ4 = 45arrow_forward
- Chapter 4 Quiz 2 As always, show your work. 1) FindΘgivencscΘ=1.045. 2) Find Θ given sec Θ = 4.213. 3) Find Θ given cot Θ = 0.579. Solve the following three right triangles. B 21.0 34.6° ca 52.5 4)c 26° 5) A b 6) B 84.0 a 42° barrow_forwardQ1: A: Let M and N be two subspace of finite dimension linear space X, show that if M = N then dim M = dim N but the converse need not to be true. B: Let A and B two balanced subsets of a linear space X, show that whether An B and AUB are balanced sets or nor. Q2: Answer only two A:Let M be a subset of a linear space X, show that M is a hyperplane of X iff there exists ƒ€ X'/{0} and a € F such that M = (x = x/f&x) = x}. fe B:Show that every two norms on finite dimension linear space are equivalent C: Let f be a linear function from a normed space X in to a normed space Y, show that continuous at x, E X iff for any sequence (x) in X converge to Xo then the sequence (f(x)) converge to (f(x)) in Y. Q3: A:Let M be a closed subspace of a normed space X, constract a linear space X/M as normed space B: Let A be a finite dimension subspace of a Banach space X, show that A is closed. C: Show that every finite dimension normed space is Banach space.arrow_forward• Plane II is spanned by the vectors: P12 P2 = 1 • Subspace W is spanned by the vectors: W₁ = -- () · 2 1 W2 = 0arrow_forward
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