Question

solve the solution
2x + 3 = 2x + 7


and how many solutions does it have

Answer 1

do the same for this 7x + 3 = 7x + 3

Answer 2

same for this 4x+22=8x+10

Answer 3

5x+5=5x+4

Answer 4

To solve the equation \( 2x + 3 = 2x + 7 \), we can start by attempting to isolate \( x \).

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

This statement \( 3 = 7 \) is false.

Since we arrived at a contradiction, this means that the original equation has **no solutions**. Thus, the equation is inconsistent.

Answer 5

To solve the equation \( 7x + 3 = 7x + 3 \), we follow similar steps to isolate \( x \).

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

This statement \( 3 = 3 \) is always true.

Since the equation holds true for any value of \( x \), it indicates that there are **infinitely many solutions** for this equation. In this case, any value of \( x \) will satisfy the equation.

Answer 6

To solve the equation \( 4x + 22 = 8x + 10 \), we can isolate \( x \) by following these steps:

1. Subtract \( 4x \) from both sides:
\[
4x + 22 - 4x = 8x + 10 - 4x
\]
which simplifies to:
\[
22 = 4x + 10
\]

2. Next, subtract \( 10 \) from both sides:
\[
22 - 10 = 4x + 10 - 10
\]
which simplifies to:
\[
12 = 4x
\]

3. Now, divide both sides by \( 4 \):
\[
\frac{12}{4} = x
\]
which simplifies to:
\[
x = 3
\]

So, the solution to the equation \( 4x + 22 = 8x + 10 \) is \( x = 3 \).

Since we found a specific value for \( x \), this equation has **one solution**.

Answer 7

To solve the equation \( 5x + 5 = 5x + 4 \), we can isolate \( x \) by following these steps:

1. Subtract \( 5x \) from both sides:
\[
5x + 5 - 5x = 5x + 4 - 5x
\]
This simplifies to:
\[
5 = 4
\]

The statement \( 5 = 4 \) is false, which indicates that the original equation has no solutions.

Thus, the equation \( 5x + 5 = 5x + 4 \) is inconsistent, and it has **no solutions**.