Solve the equation. Please show the process to solve.

Question

2x + 3 = 2x + 7
How many solutions does this equation have? Circle below.
None
One
Infinite

Answer 1

To solve the equation \(2x + 3 = 2x + 7\), we will follow these steps:

1. Isolate the variable: Start with the equation: \[ 2x + 3 = 2x + 7 \]

2. Subtract \(2x\) from both sides: \[ 2x + 3 - 2x = 2x + 7 - 2x \] This simplifies to: \[ 3 = 7 \]

3. Analyze the result: The equation \(3 = 7\) is a false statement.

Since we arrived at a contradiction, this means that there are no values for \(x\) that will satisfy the original equation. Therefore, the equation has:

None (no solutions).

So, to answer your question:

• The equation has None solutions.

Answer 2

give a more detailed answer

Answer 3

Certainly! Let’s go through the process of solving the equation \(2x + 3 = 2x + 7\) step by step with detailed explanations for each step.

Step 1: Write Down the Original Equation

We start with the given equation: \[ 2x + 3 = 2x + 7 \]

Step 2: Simplify the Equation

Our goal is to isolate \(x\) on one side of the equation. To begin, we can try to eliminate \(2x\) from both sides. This helps us see if there are any values of \(x\) that satisfy the equation.

Step 3: Subtract \(2x\) from Both Sides

We subtract \(2x\) from each side of the equation: \[ (2x + 3) - 2x = (2x + 7) - 2x \] This simplifies to: \[ 3 = 7 \]

Step 4: Analyze the Result

Now we have the statement \(3 = 7\). This is clearly a contradiction—it’s not a true statement.

Step 5: Conclusion

Because we reached a contradiction, it indicates that there are no values of \(x\) that can make the original equation true. In the context of algebra, when an equation simplifies to a false statement like \(3 = 7\), it tells us that the two sides of the original equation will never be equal regardless of the value assigned to \(x\).

Final Result

As a result, we conclude that the equation \(2x + 3 = 2x + 7\) has:

None (no solutions).

In summary:

• If two expressions are set equal and simplifying leads to a false statement, the equation has no solutions.
• We confirm that the correct answer is None.

Answer 4

Use the excerpt to answer the question.

A government of our own is our natural right: And when a man seriously reflects on the precariousness of human affairs, he will become convinced, that it is infinitely wiser and safer, to form a constitution of our own in a cool deliberate manner, while we have it in our power, than to trust such an interesting event to time and chance.— Thomas Paine, Common Sense

What effect do you think these words had on the American colonists?

(1 point)
Responses

They most likely encouraged the Framers to meet and write the U.S. Constitution at the Continental Congress.
They most likely encouraged the Framers to meet and write the U.S. Constitution at the Continental Congress.

They most likely strengthened the colonists’ desire to act on their wish to separate from Britain.
They most likely strengthened the colonists’ desire to act on their wish to separate from Britain.

They most likely increased colonial acts of civil disobedience by confirming their validity
They most likely increased colonial acts of civil disobedience by confirming their validity

They most likely inspired fear in the Loyalists of the Patriots

What significant effect did the Treaty of Paris, signed after the French and Indian War, have on France?(1 point)
Responses

France lost its claim to the entire Florida territory.
France lost its claim to the entire Florida territory.

France had to allow the British to claim and settle the Ohio Valley.
France had to allow the British to claim and settle the Ohio Valley.

France had lost most of its territory and power in North America.
France had lost most of its territory and power in North America.

France had to withdraw to its empire in Central and South America.
France had to withdraw to its empire in Central and South America.

Which of the following excerpts is a grievance of the American colonists that was included in the Declaration of Independence?(1 point)
Responses

“He has dissolved Representative Houses repeatedly, for opposing with manly firmness his invasions on the rights of the people.”
“He has dissolved Representative Houses repeatedly, for opposing with manly firmness his invasions on the rights of the people.”

“Such has been the patient sufferance of these Colonies; and such is now the necessity which constrains them to alter their former Systems of Government.”
“Such has been the patient sufferance of these Colonies; and such is now the necessity which constrains them to alter their former Systems of Government.”

“We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness."
“We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness."

“We, therefore, the Representatives of the United States of America. . . solemnly publish and declare, That these United Colonies are, and of Right ought to be Free and Independent States. . . .”

Use the excerpt to answer the question.

. . . I long to hear that you have declared an independency—and by the way in the new Code of Laws which I suppose it will be necessary for you to make I desire you would Remember the Ladies, and be more generous and favorable to them than your ancestors. . . . If particular care and attention is not paid to the Ladies we are determined to foment [incite; instigate] a Rebellion, and will not hold ourselves bound by any Laws in which we have no voice, or Representation. . . .

—Abigail Adams, letter to John Adams

How does Abigail Adams use the ideas of the patriots to support her cause?

(1 point)
Responses

by comparing the existing British laws with the laws that the patriots feel need to be established
by comparing the existing British laws with the laws that the patriots feel need to be established

by insisting that history has always been unfair to women
by insisting that history has always been unfair to women

by declaring women to be independent from and having the same rights as men
by declaring women to be independent from and having the same rights as men

by claiming that women have the right to rebel if they do not have a voice in government
by claiming that women have the right to rebel if they do not have a voice in government

What motivated most African American soldiers to fight in the Revolutionary War with the Patriots?(1 point)
Responses

the need to protect their family and the families of their masters
the need to protect their family and the families of their masters

the hope that the war would also bring an end to slavery
the hope that the war would also bring an end to slavery

the fear of what would happen if they did not fight in the war
the fear of what would happen if they did not fight in the war

the desire to achieve military ranks

Answer 5

Here are the responses to the questions based on the excerpts and context provided:

Effect of Paine's Words on American Colonists

Response: They most likely strengthened the colonists’ desire to act on their wish to separate from Britain.

• Explanation: Thomas Paine’s argument in "Common Sense" advocates for independence and creating a government that reflects the people's rights. His emphasis on forming a constitution rather than relying on chance would resonate deeply with colonists who were frustrated with British rule, thereby motivating them to pursue separation.

Impact of the Treaty of Paris on France

Response: France had lost most of its territory and power in North America.

• Explanation: The Treaty of Paris (1763) concluded the French and Indian War, resulting in France ceding significant lands to Britain, notably Canada and territory east of the Mississippi River, which diminished France's influence and power in North America.

Grievance Included in the Declaration of Independence

Response: “He has dissolved Representative Houses repeatedly, for opposing with manly firmness his invasions on the rights of the people.”

• Explanation: This excerpt reflects a specific grievance against King George III, addressing the lack of representation and rights that was central to the colonists' discontent, making it a key component of the Declaration of Independence.

Abigail Adams and the Ideas of the Patriots

Response: by claiming that women have the right to rebel if they do not have a voice in government.

• Explanation: Abigail Adams uses the language of rebellion commonly used by patriots to argue for women’s rights. She asserts that if women are not given representation in the new laws, they too have the right to rebel, paralleling the patriots' arguments against British authority.

Motivation of African American Soldiers

Response: the hope that the war would also bring an end to slavery.

• Explanation: Many African American soldiers were motivated by the belief that their participation in the Revolutionary War might lead to greater rights for themselves and the hope of an end to slavery, based on the rhetoric of freedom and equality that was prevalent among the patriots.

These answers align with historical context and reflect the sentiments and motivations expressed at the time.