For the equation to have infinite solutions, the coefficients of x in both terms must be equal.
Therefore, 4x + 10 = 1x + 10
omplete the equation so that it has infinite solutions.(1 point)
4x+10= _x+ _
11 answers
Which of the following is an example of an equation with no solution?(1 point)
Responses
3x+4=4x+3
3 x plus 4 equals 4 x plus 3
4x+3=3x+3
4 x plus 3 equals 3 x plus 3
3x+4=3x+3
3 x plus 4 equals 3 x plus 3
3x+4=3x+4
Responses
3x+4=4x+3
3 x plus 4 equals 4 x plus 3
4x+3=3x+3
4 x plus 3 equals 3 x plus 3
3x+4=3x+3
3 x plus 4 equals 3 x plus 3
3x+4=3x+4
The correct option is:
3x + 4 = 3x + 4.
This equation has no solution because when we simplify it, we get 0 = 0. This means that both sides of the equation are equal for any value of x.
3x + 4 = 3x + 4.
This equation has no solution because when we simplify it, we get 0 = 0. This means that both sides of the equation are equal for any value of x.
Which of the following is an example of an equation with exactly one solution?(1 point)
Responses
3x+4=3x+3
3 x plus 4 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
4x+3=4x+3
Responses
3x+4=3x+3
3 x plus 4 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
4x+3=4x+3
The correct option is:
3x + 4 = 4x + 3.
In this equation, we can solve for x and find a unique solution. The variable x has a specific value that satisfies the equation.
3x + 4 = 4x + 3.
In this equation, we can solve for x and find a unique solution. The variable x has a specific value that satisfies the equation.
Justify why −12(x−3)−52=−16 has one solution, infinitely many solutions, or no solution.(1 point)
Responses
It has infinitely many solutions because the solution is in the form a=a.
It has infinitely many solutions because the solution is in the form a equals a .
It has no solution because the solution is in the form a=b.
It has no solution because the solution is in the form a equals b .
It has one solution, because the solution is in the form x=a. The solution is x=−12.
It has one solution, because the solution is in the form x equals a . The solution is x equals negative 12 .
It has one solution because the solution is in the form x=a. The solution is x=0.
Responses
It has infinitely many solutions because the solution is in the form a=a.
It has infinitely many solutions because the solution is in the form a equals a .
It has no solution because the solution is in the form a=b.
It has no solution because the solution is in the form a equals b .
It has one solution, because the solution is in the form x=a. The solution is x=−12.
It has one solution, because the solution is in the form x equals a . The solution is x equals negative 12 .
It has one solution because the solution is in the form x=a. The solution is x=0.
The correct option is:
It has one solution because the solution is in the form x=a. The solution is x=−12.
To solve the equation, we can start by distributing the negative sign to the terms inside the parentheses:
-12(x - 3) - 52 = -16
-12x + 36 - 52 = -16
Next, we can combine like terms:
-12x - 16 = -16
Finally, we isolate the variable by adding 16 to both sides of the equation:
-12x = 0
Dividing both sides by -12, we find:
x = -12
Therefore, the equation has one solution, and that solution is x = -12.
It has one solution because the solution is in the form x=a. The solution is x=−12.
To solve the equation, we can start by distributing the negative sign to the terms inside the parentheses:
-12(x - 3) - 52 = -16
-12x + 36 - 52 = -16
Next, we can combine like terms:
-12x - 16 = -16
Finally, we isolate the variable by adding 16 to both sides of the equation:
-12x = 0
Dividing both sides by -12, we find:
x = -12
Therefore, the equation has one solution, and that solution is x = -12.
Solve for x to determine if the equation has one, none, or infinite solutions.
3(x+2)−6=3x(1 point)
Responses
The equation has no solution.
The equation has no solution.
The equation has one solution: x=−3.
The equation has one solution: x equals negative 3 .
The equation has infinite solutions.
The equation has infinite solutions.
The equation has one solution: x=3.
3(x+2)−6=3x(1 point)
Responses
The equation has no solution.
The equation has no solution.
The equation has one solution: x=−3.
The equation has one solution: x equals negative 3 .
The equation has infinite solutions.
The equation has infinite solutions.
The equation has one solution: x=3.
The correct option is:
The equation has no solution.
To solve this equation, we can start by distributing the 3 on the left side of the equation:
3(x + 2) - 6 = 3x
3x + 6 - 6 = 3x
The +6 and -6 cancel each other out, leaving:
3x = 3x
Since the variable term is the same on both sides, we can subtract 3x from both sides of the equation:
0 = 0
This equation is always true, meaning that it applies to all values of x. Therefore, it does not have one specific solution. Instead, it has no solution.
The equation has no solution.
To solve this equation, we can start by distributing the 3 on the left side of the equation:
3(x + 2) - 6 = 3x
3x + 6 - 6 = 3x
The +6 and -6 cancel each other out, leaving:
3x = 3x
Since the variable term is the same on both sides, we can subtract 3x from both sides of the equation:
0 = 0
This equation is always true, meaning that it applies to all values of x. Therefore, it does not have one specific solution. Instead, it has no solution.
Solve for x to determine if the equation has one, none, or infinite solutions.
4x=3(x+5)−15 (1 point)
Responses
The equation has infinite solutions.
The equation has infinite solutions.
The equation has one solution: x=0.
The equation has one solution: x equals 0 .
The equation has one solution: x=−10.
The equation has one solution: x equals negative 10 .
The equation has no solution.
4x=3(x+5)−15 (1 point)
Responses
The equation has infinite solutions.
The equation has infinite solutions.
The equation has one solution: x=0.
The equation has one solution: x equals 0 .
The equation has one solution: x=−10.
The equation has one solution: x equals negative 10 .
The equation has no solution.
The correct option is:
The equation has one solution: x = -10.
To solve this equation, we can start by distributing the 3 on the right side of the equation:
4x = 3x + 15 - 15
Simplifying further, we have:
4x = 3x
Subtracting 3x from both sides of the equation, we get:
4x - 3x = 0
Simplifying further, we have:
x = 0
Therefore, the equation has one solution, and that solution is x = 0.
The equation has one solution: x = -10.
To solve this equation, we can start by distributing the 3 on the right side of the equation:
4x = 3x + 15 - 15
Simplifying further, we have:
4x = 3x
Subtracting 3x from both sides of the equation, we get:
4x - 3x = 0
Simplifying further, we have:
x = 0
Therefore, the equation has one solution, and that solution is x = 0.
2 answers