Which of the following is an example of an equation with no solution?
4x+3=3x+3
3x+4=4x+3
3x+4=3x+3
3x+4=3x+4
The equation "3x+4=3x+4" is an example of an equation with no solution.
Which of the following is an example of an equation with exactly one solution?
3x+4=4x+3
3x+4=3x+4
3x+4=3x+3
4x+3=4x+3
The equation "4x+3=4x+3" 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
The equation has no solution.
The equation has one solution: x=3.
The equation has infinite solutions.
The equation has one solution: x=−3.
To solve the equation 3(x+2)-6=3x, we can distribute the 3 to the terms inside the parentheses:
3x + 6 - 6 = 3x
The +6 and -6 cancel each other out, leaving us with:
3x = 3x
This equation simplifies to 0 = 0.
Since this equation is always true, it means that any value of x will satisfy the equation. Therefore, the equation has infinite solutions.
Solve for x to determine if the equation has one, none, or infinite solutions.
4x=3(x+5)−15
The equation has one solution: x=0.
The equation has one solution: x=−10.
The equation has infinite solutions.
The equation has no solution.
To solve the equation 4x = 3(x+5) - 15, we can distribute the 3 to the terms inside the parentheses:
4x = 3x + 15 - 15
Simplifying further, we have:
4x = 3x
Subtracting 3x from both sides, we get:
x = 0
Therefore, the equation has one solution: x = 0.
Solve for x to determine if the equation has one, none, or infinite solutions.
5(2x+2)−7x=3x+6
The equation has no solution.
The equation has one solution: x=10.
.
The equation has infinite solutions.
The equation has one solution: x=6.
To solve the equation 5(2x+2) - 7x = 3x + 6, we first distribute the 5 to the terms inside the parentheses:
10x + 10 - 7x = 3x + 6
Combining like terms, we have:
3x + 10 = 3x + 6
Now, we can subtract 3x from both sides to eliminate the variable:
10 = 6
This equation is not true, which means there is no solution that satisfies both sides of the equation.
Therefore, the equation has no solution.
To determine if an equation has a solution, we need to simplify and compare the coefficients of the variables on both sides of the equation.
Let's examine each equation to see if there is a solution:
1) 4x + 3 = 3x + 3
To solve this equation, we can start by rearranging the terms:
4x - 3x = 3 - 3
x = 0
Since x equals 0, the equation has a solution.
2) 3x + 4 = 4x + 3
Rearranging the equation, we have:
3x - 4x = 3 - 4
-x = -1
Multiplying both sides by -1, we get:
x = 1
The equation has a solution since x equals 1.
3) 3x + 4 = 3x + 3
By rearranging the terms:
3x - 3x = 3 - 4
0 = -1
In this case, the equation has no solution because the equation simplifies to 0 = -1, which is not possible.
4) 3x + 4 = 3x + 4
Rearranging the equation:
3x - 3x = 4 - 4
0 = 0
This equation is an example of an identity, where the variables cancel out, resulting in 0 = 0. While this equation is true, it does not provide any specific solutions for x.
Therefore, the correct answer is:
3x + 4 = 3x + 3