solve 7x + 3 = 7x + 3
11 answers
This equation is already solved. Both sides of the equation are equal, so the solution is all real numbers.
What does it mean to have infinite solutions?
Having infinite solutions means that any value of the variable will satisfy the equation. In this case, since both sides of the equation are identical (7x + 3), any value of x will make the equation true. This concept is often encountered when dealing with equations that are identities, where both sides are always equal, regardless of the variable value.
solve 2x + 3 = 2x + 7
and solve 5x + 5 = 5x + 4
and solve 5x + 5 = 5x + 4
For the equation 2x + 3 = 2x + 7:
Subtracting 2x from both sides:
3 = 7
Since this yields a false statement (3 is not equal to 7), this equation has no solution. There are no real numbers that can make this equation true because the left and right sides are not equal.
For the equation 5x + 5 = 5x + 4:
Subtracting 5x from both sides:
5 = 4
Again, this yields a false statement (5 is not equal to 4), so this equation also has no solution.
Subtracting 2x from both sides:
3 = 7
Since this yields a false statement (3 is not equal to 7), this equation has no solution. There are no real numbers that can make this equation true because the left and right sides are not equal.
For the equation 5x + 5 = 5x + 4:
Subtracting 5x from both sides:
5 = 4
Again, this yields a false statement (5 is not equal to 4), so this equation also has no solution.
What does it mean to have no solutions?
Having no solutions means that there are no possible values of the variable that will make the equation true. In other words, there is no real number that can satisfy the equation. This usually occurs when the equation leads to a contradiction, such as 3 = 7 or 5 = 4, as in the examples provided. These types of equations have no solution because no value of the variable will ever make the equation true.
Consider the two equations that you underlined, with one solution. Solve the equations.
3x + 18 = 5x + 8 4x + 22 = 8x + 10
3x + 18 = 5x + 8 4x + 22 = 8x + 10
Sure, here are the solutions for the two equations:
1. 3x + 18 = 5x + 8
Subtracting 3x from both sides:
18 = 2x + 8
Subtracting 8 from both sides:
10 = 2x
Dividing by 2:
x = 5
Therefore, the solution for the first equation is x = 5.
2. 4x + 22 = 8x + 10
Subtracting 4x from both sides:
22 = 4x + 10
Subtracting 10 from both sides:
12 = 4x
Dividing by 4:
x = 3
Therefore, the solution for the second equation is x = 3.
1. 3x + 18 = 5x + 8
Subtracting 3x from both sides:
18 = 2x + 8
Subtracting 8 from both sides:
10 = 2x
Dividing by 2:
x = 5
Therefore, the solution for the first equation is x = 5.
2. 4x + 22 = 8x + 10
Subtracting 4x from both sides:
22 = 4x + 10
Subtracting 10 from both sides:
12 = 4x
Dividing by 4:
x = 3
Therefore, the solution for the second equation is x = 3.
smaller summary
Sure, here is a summary of the solutions to the two equations:
1. 3x + 18 = 5x + 8 has a solution of x = 5.
2. 4x + 22 = 8x + 10 has a solution of x = 3.
1. 3x + 18 = 5x + 8 has a solution of x = 5.
2. 4x + 22 = 8x + 10 has a solution of x = 3.
1 answer