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

**Page 111 Exercise 3 Answer**

It is given that Edy has $450 in her saving account.

After how many months will Edy and Juan have the same amount of money in their accounts

Let the time at which Edy and Juan will have same amount of money be x. So, according to given question:

After 5 months, Edy and Juan will have same amount of money in their accounts.

**Page 111 Exercise 4 Answer**

Infinite many solution means that every value is the solution of the given equation.

The equation that has infinite many solution is:

Option c is correct.

**Page 111 Exercise 5 Answer**

The given equation is −4(x − 1) + 6x = 34

To find: solve the given equation

The value of x is 15.

**Page 111 Exercise 6 Answer**

Hakeem subtracted 8 from a number, then multiplied the difference by 5. So, the result was 20.

The value of x is 12.

**Page 112 Exercise 1 Answer**

It is given that the race is of 42 miles and hector is completed 18 miles at a speed of 12 miles per hour.

Let x be the hours needed for Wanda to catch up with Hector.

Hector has already completed 18 miles at a speed of 12 miles per hour.

So, after x more hours, Hector will travel 18 + 12x miles.

Wanda travels at 16 miles per hour. In x hours, she travel 16x miles.

If Wanda catches up to Hector, then

16x = 18 + 12x

4x = 18

x = 4.5 hours.

Wanda will catch up to Hector in 4 hours and 30 minutes.

It is given that the race is of 42 miles and hector is completed 18 miles at a speed of 12 miles per hour.

Wanda will catch up to Hector at 16x miles, i.e. 72 miles.

But the race is of 42 miles. So, Wanda will catch up to Hector after the race.

Wanda will not catch up to Hector before the race is completed.

It is given that the race is of 42 miles and hector is completed 18 miles at a speed of 12 miles per hour.

Distance till finish line is 42 miles.

The speed at which Wanda is travelling is 16 miles per hour.

The speed Wanda should travel = \(\frac{42}{16}=2.625\) miles per hour.

Wanda could travel at a constant speed of 2.625 miles per hour to catch up Hector at the finish line.

**Page 113 Exercise 1 Answer**

The video mentioned above shown some images that predict the charge left in the laptop before it completely drained off.

The device runs out of power and the battery percentage is dropping.

The charger was left at home so the laptop runs only for certain hours.

The reason is for knowing the amount of time left for a certain percentage of charge left in the laptop.

You may frequently utilize visual cues to figure out what’s in the shot and what the remainder of the thing could appear like.

The first question that comes to my mind after watching this video is “How much time is left before the laptop charge completely drained off?”.

“How much time is left before the laptop charge completely drained off?”.

This is the question that made up my mind after watching this video.

**Page 113 Exercise 2 Answer**

The video mentioned above shown some images that predict the charge left in the laptop before it completely drained off.

The device runs out of power and the battery percentage is dropping.

The charger was left at home so the laptop runs only for certain hours.

The reason is for knowing the amount of time left for a certain percentage of charge left in the laptop.

You may frequently utilize visual cues to figure out what’s in the shot and what the remainder of the thing could appear like.

The first question that comes to my mind after watching this video is “How much time is left before the laptop charge completely drained off?”.

The main question that I will answer that I saw in the video is “How much time is left before the laptop charge completely drained off?”.

**Page 113 Exercise 3 Answer**

A conjecture is a result or statement in math that is thought to be valid based on basic evidence to back it up but for which no evidence or falsifiability has ever been produced.

A conjecture is nothing but a conclusion we made up where it doesn’t have any proof to make it false.

The charger was left at home so the laptop runs only for certain hours.

The reason is for knowing the amount of time left for a certain percentage of charge left in the laptop.

The first question that comes to my mind after watching this video is “How much time is left before the laptop charge completely drained off?”.

The laptop will run 8 hours when it is fully charged. The charge left now is 25%.

Hence, it can run another two hours before it completely drained off.

An answer that I was predicted to this main question is two hours.

An answer that I was predicted to this main question is two hours. I found my answer by evaluating the 25% of 8 hours.

= 2 hours

**Page 113 Exercise 5 Answer**

Informally, a conjecture is simply making judgments over something based on what you understand and monitor.

A conjecture is a declaration that is thought to be accurate based on data.

In general, a conjecture is your view or an informed guess over something you recognize.

You can’t indicate any of it; you simply observed a pattern and conclude.

A number that I know which is too early to be the answer is 0 hours since the charge is still remaining hence we cannot say it is completely drained.

A number that is too late to be the answer is 8 hours since it can only happen when the charge is full. We know that the charge has already drained up to a certain percent.

My prediction is two hours.

Plotting my prediction on the same number line, I get,

**Page 114 Exercise 6 Answer**

Informally, a conjecture is simply making judgments over something based on what you understand and monitor.

A conjecture is a declaration that is thought to be accurate based on data.

In general, a conjecture is your view or an informed guess over something you recognize.

You can’t indicate any of it; you simply observed a pattern and conclude.

In this situation, information regarding the number of hours it took for the laptop to completely charge is more helpful to know.

This is because I can use that information to charge my laptop completely using another charger and I can continue with my work.

In this situation, information regarding the number of hours it took for the laptop to completely charge is more helpful to know. I can use that information to charge my laptop completely.

**Page 114 Exercise 7 Answer**

Informally, a conjecture is simply making judgments over something based on what you understand and monitor.

A conjecture is a declaration that is thought to be accurate based on data.

In general, a conjecture is your view or an informed guess over something you recognize.

You can’t indicate any of it; you simply observed a pattern and conclude.

To get the information I need regarding the number of hours it took to charge, I can use a similar charger to charge it and calculate the number of percentages charged for every 5 mins to calculate how long it will take to charge completely.

A charger can be used to get the information I need. The laptop took 1.5 hours to charge completely.

**Page 114 Exercise 8 Answer**

A conjecture is a result or statement in math that is thought to be valid based on basic evidence to back it up but for which no evidence or falsifiability has ever been produced.

A conjecture is nothing but a conclusion we made up where it doesn’t have any proof to make it false.

The following steps are used to refine my conjecture:

Measure the number of hours left before it completely drained off.

Recognize each one of the conjecture’s circumstances – The situations of a conjecture are the requirements that must be met already when we acknowledge the conjecture’s findings.

Create both examples and non-examples – Find items that meet the criteria and verify to see if they also fulfill the conjecture’s inference. Start by removing each situation one at a time and build non-examples that gratify the other circumstances but not the inference.

Seek out counterexamples – A counterexample meets all of the circumstances of a statement except the conclusion.

Try comparing yours with others.

From this way, I have found out that the charge left can make the laptop run for two more hours.

**Page 114 Exercise 9 Answer**

A conjecture is a declaration that is thought to be accurate based on data.

In general, a conjecture is your view or an informed guess over something you recognize.

You can’t indicate any of it; you simply observed a pattern and conclude.

The charger was left at home so the laptop runs only for certain hours.

We need to calculate the number of hours left for the laptop before it gets completely drained off.

An answer that I was predicted is 2 hours.

This is the same as my prediction.

The answer to the Main Question is two hours. It is equal to my prediction.

**Page 115 Exercise 10 Answer**

A conjecture is a result or statement in math that is thought to be valid based on basic evidence to back it up but for which no evidence or falsifiability has ever been produced.

A conjecture is nothing but a conclusion we made up where it doesn’t have any proof to make it false.

The charger was left at home so the laptop runs only for certain hours.

We need to calculate the number of hours left for the laptop before it gets completely drained off.

An answer that I was predicted is 2 hours.

This is the same as my prediction.

The answer that I saw in the video is also the same.

The answer that I saw in the video is two hours.

**Page 115 Exercise 11 Answer**

The charger was left at home so the laptop runs only for certain hours.

We need to calculate the number of hours left for the laptop before it gets completely drained off.

An answer that I was predicted is two hours.

This is the same as my prediction.

My answer matches the answer in the video. This is because the number of hours can be easily determined by the battery percentage.

My answer matches the answer in the video. This is because the number of hours can be easily determined by the battery percentage.

**Page 115 Exercise 12 Answer**

The charger was left at home so the laptop runs only for certain hours.

We need to calculate the number of hours left for the laptop before it gets completely drained off.

An answer that I was predicted is two hours.

This is the same as my prediction.

My answer matches the answer in the video. This is because the number of hours can be easily determined by the battery percentage.

I’m not going to change my model.

No, I would not change my model now that I know the answer.

**Page 116 Exercise 13 Answer**

The following steps are used to refine my conjecture:

Measure the number of hours left before it completely drained off.

Recognize each one of the conjecture’s circumstances – The situations of a conjecture are the requirements that must be met already when we acknowledge the conjecture’s findings.

Create both examples and non-examples – Find items that meet the criteria and verify to see if they also fulfill the conjecture’s inference. Start by removing each situation one at a time and build non-examples that gratify the other circumstances but not the inference.

Seek out counterexamples – A counterexample meets all of the circumstances of a statement except the conclusion.

Try comparing yours with others.

The model helps me answer the Main Question by making an accurate calculation of battery percentage and the number of hours the battery remains when it is fully charged and to know the number of hours left before it completely drained off.

**Page 116 Exercise 15 Answer**

After 35 minutes, he started charging his phone. 21 minutes later, the battery is at 23%.