## Envision Math Grade 8 Student Solutions Volume 1 Chapter 2 Analyze And Solve Linear Equations

**Page 97 Exercise 1 Answer**

Given

Water flows through one pipe at a rate of 25,000 gallons an hour and through the other pipe at 45,000 gallons an hour.

To find/solve

Water leaves the system at a rate of 60,000 gallons an hour.

We have to write an equation where the variable will be the gallons that are leaving and entering the system per hour. The right side of the equation will have the maximum amount of gallons the tank can holes.

If we are asked to find the time needed for 3 tanks we simply multiply 50.3 = 150 hours

150 hours.is required to fill 3 tanks

**Page 97 Exercise 1 Answer**

Given

Statement

To find/solve.

The bar model is a pictorial representation of a problem or concept where bars or boxes are used to represent the known and unknown quantities.

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.

Yes, it is basically a graphical representation of data using bars of different heights. In real life, bar graphs are commonly used to represent business data.

Yes, it is basically a graphical representation of data using bars of different heights. In real life, bar graphs are commonly used to represent business data.

**Page 97 Exercise 1 Answer**

Given

Expression 4(3x + 7x − 5)

To find/solve

Equals 40x − 20.

In the task it should say to simplify given expression so that it would be equal to

40x + 20, not 4x − 20

First way to simplify the expression:

4(3x + 7x + 5)

We get 4(10x + 5)

Then 40x + 20

Next to multiply 4 by the terms inside the parentheses

4(3x + 7x + 5)

12x + 28x + 20

First way is to combine like terms and then multiply 4 with the terms inside the parentheses. The second way is to multiply 4 with the terms inside the parentheses and then combine like terms.

First way is to combine like terms and then multiply 4 with the terms inside the parentheses. The second way is to multiply 4 with the terms inside the parentheses and then combine like terms.

**Page 98 Question 1 Answer**

To find/solve: How can you use the Distributive Property to solve multistep equations?

When we are solving multistep equations, distributive property helps us with solving parentheses

Example

2(3x + 3) = 7

In the given equation, we use the distributive property so we can solve the parentheses.

2.3x + 2.3 = 7

When we are solving multistep equations, distributive property helps us with solving parentheses.

**Page 98 Exercise 1 Answer**

To find/solve: How can you find the solution of the equation using the bar diagram?

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.

The bar model is a pictorial representation of a problem or concept where bars or boxes are used to represent the known and unknown quantities.

Bar models are most often used to solve number problems with the four operations- addition and subtraction, multiplication and division.

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.

The bar model is a pictorial representation of a problem or concept where bars or boxes are used to represent the known and unknown quantities.

**Page 99 Exercise 2 Answer**

Given

\(-3(-7-x)=\frac{1}{2}(x+2)\)To find/solve

In the first step, we have to solve brackets on both sides

Here x = -8

x = -8 is the required answer

**Page 98 Exercise 1 Answer**

Given: can u add x to -5x on the left side of the equation as the first step

To find/solve: explain the given statement

First, we have to multiply the value in front of the parentheses with values in brackets

No we can’t add x to −5x on the left side of the equation as the first step because parentheses have higher priority than subtracting. First we need to solve the parentheses. Subtracting and adding our last operations to priority list.

No we can’t add x to −5x on the left side of the equation as the first step because parentheses have higher priority than subtracting. First we need to solve the parentheses. Subtracting and adding are the last operations on priority list.

**Page 100 Exercise 2 Answer**

Given

3(3x – 5x) + 2 = −8

To find: first step when solving the equation

The first step is to combine like terms in the parenthesis

3(3x − 5x) + 2 = −8

3.(−2x) + 2 = −8

The first step is to combine like terms in the parenthesis.

**Page 100 Exercise 4 Answer**

The given equation is 3x + 2 = x + 4(x + 2)

We need to solve the given equation.

The value of x = −3

**Page 100 Exercise 5 Answer**

The given equation is −3(x − 1) + 7x = 27

We need to solve the given equation.

The value of x = 6

**Page 100 Exercise 7 Answer**

The given equation is 0.25(x + 4) − 3 = 28

We need to solve the given equation.

The value of x = 120

**Page 101 Exercise 8 Answer**

Given that, Lori bought a shirt and a hat at a half-off sale. If she spent a total of $21 on the two items, we need to find the original price of the hat.

The original price of the shirt is $24

The original price of the hat is x

Given that these are sold at a half rate and the total money spent is $21

The original price of the hat is $18

**Page 101 Exercise 9 Answer**

We need to use the Distributive Property to solve the given equation 28 − (3x + 4) = 2(x + 6) + x

The given is, 28−(3x+4)=2(x+6)+x

The value of x = 2

**Page 101 Exercise 10 Answer**

We need to use the Distributive Property to solve the given equation 3(x − 6) + 6 = 5x − 6

The given equation is, 3(x − 6) + 6 = 5x − 6

The value of x = −3

**Page 102 Exercise 15 Answer**

We need to use the Distributive Property to solve the given equation 4x − 2(x − 2) = −9 + 5x − 8

The given equation is, 4x − 2(x − 2) = −9 + 5x − 8

Solving the given using the distributive property, we get,

The value of x = 7

**Page 102 Exercise 16 Answer**

We need to use the Distributive Property to solve the equation 2(m + 2) = 22

We need to describe what it means to distribute the 2 to each term inside the parentheses.

The given equation is, 2(m + 2) = 22

Solving the given using the distributive property, we get,

The value of m = 9

We need to multiply two to each one of the terms inside the parentheses to distribute the 2 to each term.

**Page 102 Exercise 17 Answer**

We need to find Peter’s number.

Let the unknown number be x

Subtract 12 from x and multiply the difference by −3

The result is −54

Thus, the equation be,

Peter’s number is 30

**Page 102 Exercise 19 Answer**

Given:

−2(x + 4) = −6

We consider:

The required solution is x = −1

**Page 102 Exercise 20 Answer**

Given:

3(x + 4) = 27

We consider:

The required solution is x = 5