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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- OR 16 f(x) = Ef 16 χ по x²-2 410 | y = (x+2) + 4 Y-INT: y = 0 X-INT: X=0 VA: x=2 OA: y=x+2 0 X-INT: X=-2 X-INT: y = 2 VA 0 2 whole. 2-2 4 y - (x+2) = 27-270 + xxx> 2 क् above OA (x+2) OA x-2/x²+0x+0 2 x-2x 2x+O 2x-4 4 X<-1000 4/4/2<0 below Of y VA X=2 X-2 OA y=x+2 -2 2 (0,0) 2 χarrow_forwardI need help solving the equation 3x+5=8arrow_forwardWhat is the domain, range, increasing intervals (theres 3), decreasing intervals, roots, y-intercepts, end behavior (approaches four times), leading coffiencent status (is it negative, positivie?) the degress status (zero, undifined etc ), the absolute max, is there a absolute minimum, relative minimum, relative maximum, the root is that has a multiplicity of 2, the multiplicity of 3.arrow_forward
- What is the vertex, axis of symmerty, all of the solutions, all of the end behaviors, the increasing interval, the decreasing interval, describe all of the transformations that have occurred EXAMPLE Vertical shrink/compression (wider). or Vertical translation down, the domain and range of this graph EXAMPLE Domain: x ≤ -1 Range: y ≥ -4.arrow_forward4. Select all of the solutions for x²+x - 12 = 0? A. -12 B. -4 C. -3 D. 3 E 4 F 12 4 of 10arrow_forward2. Select all of the polynomials with the degree of 7. A. h(x) = (4x + 2)³(x − 7)(3x + 1)4 B h(x) = (x + 7)³(2x + 1)^(6x − 5)² ☐ Ch(x)=(3x² + 9)(x + 4)(8x + 2)ª h(x) = (x + 6)²(9x + 2) (x − 3) h(x)=(-x-7)² (x + 8)²(7x + 4)³ Scroll down to see more 2 of 10arrow_forward
- 1. If all of the zeros for a polynomial are included in the graph, which polynomial could the graph represent? 100 -6 -2 0 2 100 200arrow_forward3. Select the polynomial that matches the description given: Zero at 4 with multiplicity 3 Zero at −1 with multiplicity 2 Zero at -10 with multiplicity 1 Zero at 5 with multiplicity 5 ○ A. P(x) = (x − 4)³(x + 1)²(x + 10)(x — 5)³ B - P(x) = (x + 4)³(x − 1)²(x − 10)(x + 5)³ ○ ° P(x) = (1 − 3)'(x + 2)(x + 1)"'" (x — 5)³ 51 P(r) = (x-4)³(x − 1)(x + 10)(x − 5 3 of 10arrow_forwardMatch the equation, graph, and description of transformation. Horizontal translation 1 unit right; vertical translation 1 unit up; vertical shrink of 1/2; reflection across the x axis Horizontal translation 1 unit left; vertical translation 1 unit down; vertical stretch of 2 Horizontal translation 2 units right; reflection across the x-axis Vertical translation 1 unit up; vertical stretch of 2; reflection across the x-axis Reflection across the x - axis; vertical translation 2 units down Horizontal translation 2 units left Horizontal translation 2 units right Vertical translation 1 unit down; vertical shrink of 1/2; reflection across the x-axis Vertical translation 2 units down Horizontal translation 1 unit left; vertical translation 2 units up; vertical stretch of 2; reflection across the x - axis f(x) = - =-½ ½ (x − 1)²+1 f(x) = x²-2 f(x) = -2(x+1)²+2 f(x)=2(x+1)²-1 f(x)=-(x-2)² f(x)=(x-2)² f(x) = f(x) = -2x²+1 f(x) = -x²-2 f(x) = (x+2)²arrow_forward
- What is the vertex, increasing interval, decreasing interval, domain, range, root/solution/zero, and the end behavior?arrow_forwardThe augmented matrix of a linear system has been reduced by row operations to the form shown. Continue the appropriate row operations and describe the solution set of the original system. 1 -1 0 1 -2 00-4 0-6 0 0 1 - 3 3 0 001 4arrow_forwardSolve the system. X1 - 3x3 = 10 4x1 + 2x2 + 3x3 = 22 ×2 + 4x3 = -2arrow_forward
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