Which of the following is an example of an equation with no solution?(1 point) Responses 4x+3=3x+3 4 x plus 3 equals 3 x plus 3 3x+4=3x+4 3 x plus 4 equals 3 x plus 4 3x+4=4x+3 3 x plus 4 equals 4 x plus 3 3x+4=3x+3 3 x plus 4 equals 3 x plus 3
9 answers
The equation 3x + 4 = 3x + 3 is an example of an equation with no solution.
Which of the following is an example of an equation with exactly one sol?(1 point) Responses 4x+3=3x+3 4 x plus 3 equals 3 x plus 3 3x+4=3x+4 3 x plus 4 equals 3 x plus 4 3x+4=4x+3 3 x plus 4 equals 4 x plus 3 3x+4=3x+3 3 x plus 4 equals 3 x plus 3
The equation 3x + 4 = 3x + 4 is an example of an equation with exactly one solution.
Solve for x to determine if the equation has one, none, or infinite solutions. 3(x+2)−6=3x
Let's solve the equation step-by-step:
3(x + 2) - 6 = 3x
First, distribute the 3 to both terms inside the parenthesis:
3x + 6 - 6 = 3x
Simplify the terms on the left side:
3x = 3x
We see that the variable x appears on both sides of the equation. Subtracting 3x from both sides:
3x - 3x = 0
0 = 0
In this case, the equation simplifies to 0 = 0. This means that the equation is always true, regardless of the value of x. Therefore, the equation has infinitely many solutions.
3(x + 2) - 6 = 3x
First, distribute the 3 to both terms inside the parenthesis:
3x + 6 - 6 = 3x
Simplify the terms on the left side:
3x = 3x
We see that the variable x appears on both sides of the equation. Subtracting 3x from both sides:
3x - 3x = 0
0 = 0
In this case, the equation simplifies to 0 = 0. This means that the equation is always true, regardless of the value of x. Therefore, the equation has infinitely many solutions.
Solve for x to determine if the equation has one, none, or infinite solutions. 4x=3(x+5)−15
Let's solve the equation step-by-step:
4x = 3(x + 5) - 15
First, distribute the 3 to both terms inside the parenthesis:
4x = 3x + 15 - 15
Combine like terms:
4x = 3x
We see that the variable x appears on both sides of the equation. Subtracting 3x from both sides:
4x - 3x = 0
x = 0
In this case, the variable x has a specific value, namely x = 0. Therefore, the equation has only one solution.
4x = 3(x + 5) - 15
First, distribute the 3 to both terms inside the parenthesis:
4x = 3x + 15 - 15
Combine like terms:
4x = 3x
We see that the variable x appears on both sides of the equation. Subtracting 3x from both sides:
4x - 3x = 0
x = 0
In this case, the variable x has a specific value, namely x = 0. Therefore, the equation has only one solution.
Solve for x to determine if the equation has one, none, or infinite solutions. 5(2x+2)−7x=3x+6
Let's solve the equation step-by-step:
5(2x + 2) - 7x = 3x + 6
First, distribute the 5 to both terms inside the parenthesis:
10x + 10 - 7x = 3x + 6
Combine like terms on the left side of the equation:
3x + 10 = 3x + 6
Now, let's isolate the variable terms on one side. We can do this by subtracting 3x from both sides:
10 = 6
However, we see that this equation leads to a contradiction: 10 cannot be equal to 6. Thus, there is no solution to this equation.
5(2x + 2) - 7x = 3x + 6
First, distribute the 5 to both terms inside the parenthesis:
10x + 10 - 7x = 3x + 6
Combine like terms on the left side of the equation:
3x + 10 = 3x + 6
Now, let's isolate the variable terms on one side. We can do this by subtracting 3x from both sides:
10 = 6
However, we see that this equation leads to a contradiction: 10 cannot be equal to 6. Thus, there is no solution to this equation.
2 answers