Envision Math Grade 8 Volume 1 Chapter 2 Analyze And Solve Linear Equations
Page 91 Exercise 1 Answer
We need to explain how can we use an equation to show that expressions are equal.
A bar chart or bar graph or graph that presents categorical data with rectangular bars with heights or lengths proportional to the values that they represent.
The bars can be plotted vertically or horizontally. A vertical bar chart is sometimes called a column chart.
Combine any like terms on each side of the equation: x-terms with x-terms and constant with constant.
Arrange the terms in the same are identical, then the two expressions are equivalent.
Combine any like terms on each side of the equation: x-terms with x-terms and constant with constant.
Arrange the terms in the same are identical, then the two expressions are equivalent.
Page 91 Exercise 1 Answer
We need to explain what expressions can we write to represent the amount of money collected by each boy.
Also, we need to explain how we can use these expressions to write an equation.
It seems form the picture that Jaxson has 14 checks and 15 dollars, and Bryon has 50 dollars and 7checks. It is given that each check is x dollars.
The dollar value of the checks is the number of checks times the value of each check.
Jaxson then got 14x + 15 dollars and Bryon got 50 + 7x dollars. They collected the same amount so we can set them equal to write the equation.
The equation is 14x + 15 = 50 + 7x.
Page 92 Question 1 Answer
Given
statement
To find/solve
Inverse operations.
We use inverse operations for getting all variables on one side and values on the other.
Example :
5x + 9 = 3x − 8
We subtract 3x from both sides of the equation, since 3x is on the right side of the equation.
We use inverse operations for getting all variables on one side and values on the other.
We use inverse operations for getting all variables on one side and values on the other.
Page 92 Exercise 1 Answer
Given
Class A was given a sunflower with a height of 8 centimeters that grows at a rate of \(3 \frac{1}{2}\) centimeters per week. Class B was given a sunflower with a height of 10 centimeters that grows at a rate of \(3 \frac{1}{2}\) centimeters per week.
To find/solve
After how many weeks are the sunflowers the same height?
We put the sunflower of class A on one side of the equation and the sunflower of class B on the other side of the equation. We must add variables to the rate of growth of each sunflower.
After 8 weeks the sunflowers will be the same height.
Page 93 Exercise 2 Answer
Given
96 − 4.5y − 3.2y = 5.6y + 42.80
To find/solve
We have to apply a mathematical operation to the equation until we have only variables on one side and only values on another side of the equation.
y = 4 is the required answer
Page 94 Exercise 2 Answer
Given
Statement
To find/solve
Inverse operations and properties of equality are important when solving equations.
Inverse operations help us get all variables on the same side of the equation.
Properties of equality are important because they give us a new equation that is equivalent to the original.
Properties of equality are important because they give us a new equation that is equivalent to the original.
Properties of equality are important because they give us a new equation that is equivalent to the original.
Page 94 Exercise 4 Answer
Given
Maria and Liam work in a banquet hall. Maria earns a 20% commission on her food sales. Liam earns a weekly salary of $625 plus a 10% commission on his food sales.
To find/solve
What amount of food sales will result in Maria and Liam earning the same amount for the week?
First, we have to make an equation with commissions as a variable. On one side of the equation will be Maria and on the other Liam.
6,250 dollars of food sales will result in Maria and Liam earning the same amount for the week.
6,250 dollars of food sales will result in Maria and Liam earning the same amount for the week.
Page 94 Exercise 7 Answer
The given equation is −2.6b + 4 = 0.9b − 17
We need to solve the given equation and find the value of b
Solving the equation, we get,
The value of b = 6
Page 95 Exercise 8 Answer
The given equation is 6 − 4x = 6x − 8x + 2
We need to solve the given equation and find the value of x
The value of x = 2
Page 95 Exercise 9 Answer
The given equation is \(\frac{5}{3} x+\frac{1}{3} x=13 \frac{1}{3}+\frac{8}{3} x\)
We need to solve the given equation and find the value of x
The value of x = -20
Page 95 Exercise 10 Answer
Given
Town 1 snow depth: \(3 \frac{1}{2}\) inches every hour
Town 2 snow depth: \(2 \frac{1}{4}\) inches every hour
Towns will be equal in snow depth is \(\frac{4}{5}\) of hour or 48 minutes.
Page 95 Exercise 12 Answer
The given equation is 6 − 6x = 5x − 9x − 2
We need to solve the given equation and find the value of x
The value of x = 4
Page 95 Exercise 13 Answer
Given
Each month, 200 people on average move into town. A nearby town has a population of 45,000.
To find/solve
Write an equation that represents this situation and solve.
We have to write an equation with one town on one side and the other town on another side of the equation.
In about 7 months the population of towns will be the same.
Page 96 Exercise 14 Answer
Given
statement
To find/solve
After how many months will the total cost for each health club be the same?
We have to make an equation with one health club on one side and second health club on other side of the equation.
Monthly fee will be our variable.
After 4 months.
After 4 months will the total cost for each health club be the same.
Page 96 Exercise 15 Answer
Given
The price of Stock A at 9 am. Was $12.73. since then, the price has been increasing at the rate of $0.06 per hour. At noon, the price of Stock B was $13.48. It begins to decrease at the rate of $0.14 per hour
To find/solve
How many hours will the prices of the stocks be the same?
We have to make an equation with Stock A on one side of the equation and Stock B on the other side of the equation.
We have to increase Stock A for 3 hours so that it will be growing before stock B starts falling.
After 2.85 hours Stock A and Stock B will have the same prices.
After 2.85 hours Stock A and Stock B will have the same prices.
Page 96 Exercise 16 Answer
Given
In an academic contest, correct answers earn 12 points and incorrect answers lose 5 points. In the final round, school A starts with 165 points and gives the same number of correct and incorrect answers.
To find/solve
A. Which equation models the scoring in the final round and the outcome of the contest?
On the left side of the equation will be school A. School A has 165 points from before and score 12 per correct answer and lose 5 per incorrect answer. The answers will be our variable.
165 + 12x − 5x
The second part of the equation will be school B which came into finals with 65 points, and gave only correct answer for 12 points.
12x + 65
Now we put those two expressions into same equation.
165 + 12x − 5x = 65 + 12x
165 + 12x – 5x = 65 + 12x is the required answer
Given
In an academic contest, correct answers earn 12 points and incorrect answers lose 5 points. In the final round, school A starts with 165 points and gives the same number of correct and incorrect answers.
To find/solve
How many answers did each school get correct in the final round?
On the left side of the equation will be school A. School A has 165 points from before and score 12 per correct answer and lose 5 per incorrect answer. The answers will be our variable.
165 + 12x − 5x
The second part of the equation will be school B which came into finals with 65 points, and gave only correct answer for 12 points.
12x + 65
Now we put those two expressions into same equation.
165 + 12x − 5x = 65 + 12x
First we have to write combined like terms
165 + 7x = 65 + 12x
Subtract 12x from both sides.
165 − 5x = 65
Now subtract 165 from both sides of the equation, we get
−5x = −100
x = 20
Both schools gave 20 correct answers.
Both schools gave 20 correct answers.