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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- How much is the circumference of a circle whose diameter is 7 feet?C =π darrow_forwardHow to solve 2542/64.132arrow_forwardAssume that you fancy polynomial splines, while you actually need ƒ(t) = e²/3 – 1 for t€ [−1, 1]. See the figure for a plot of f(t). Your goal is to approximate f(t) with an inter- polating polynomial spline of degree d that is given as sa(t) = • Σk=0 Pd,k bd,k(t) so that sd(tk) = = Pd,k for tk = −1 + 2 (given d > 0) with basis functions bd,k(t) = Σi±0 Cd,k,i = • The special case of d 0 is trivial: the only basis function b0,0 (t) is constant 1 and so(t) is thus constant po,0 for all t = [−1, 1]. ...9 The d+1 basis functions bd,k (t) form a ba- sis Bd {ba,o(t), ba,1(t), bd,d(t)} of the function space of all possible sα (t) functions. Clearly, you wish to find out, which of them given a particular maximal degree d is the best-possible approximation of f(t) in the least- squares sense. _ 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 -0.9 -1 function f(t) = exp((2t)/3) - 1 to project -1 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5…arrow_forward
- An image processor considered a 750×750 pixels large subset of an image and converted it into gray-scale, resulting in matrix gIn - a false-color visualization of gIn is shown in the top-left below. He prepared a two-dim. box filter f1 as a 25×25 matrix with only the 5×5 values in the middle being non-zero – this filter is shown in the top-middle position below. He then convolved £1 with itself to get £2, before convolving £2 with itself to get f3. In both of the steps, he maintained the 25×25 size. Next, he convolved gIn with £3 to get gl. Which of the six panels below shows g1? Argue by explaining all the steps, so far: What did the image processor do when preparing ₤3? What image processing operation (from gin to g1) did he prepare and what's the effect that can be seen? Next, he convolved the rows of f3 with filter 1/2 (-1, 8, 0, -8, 1) to get f4 - you find a visualization of filter f 4 below. He then convolved gIn with f4 to get g2 and you can find the result shown below. What…arrow_forward3ur Colors are enchanting and elusive. A multitude of color systems has been proposed over a three-digits number of years - maybe more than the number of purposes that they serve... - Everyone knows the additive RGB color system – we usually serve light-emitting IT components like monitors with colors in that system. Here, we use c = (r, g, b) RGB with r, g, bЄ [0,1] to describe a color c. = T For printing, however, we usually use the subtractive CMY color system. The same color c becomes c = (c, m, y) CMY (1-c, 1-m, 1-y) RGB Note how we use subscripts to indicate with coordinate system the coordinates correspond to. Explain, why it is not possible to find a linear transformation between RGB and CMY coordinates. Farbenlehr c von Goethe Erster Band. Roſt einen Defte mit fergen up Tübingen, is et 3. Cotta'fden Babarblung. ISIO Homogeneous coordinates give us a work-around: If we specify colors in 4D, instead, with the 4th coordinate being the homogeneous coordinate h so that every actual…arrow_forwardCan someone provide an answer & detailed explanation please? Thank you kindly!arrow_forward
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