Which of the following is an example of an equation with no solution?(1 point)Responses3x+4=3x+43 x plus 4 equals 3 x plus 43x+4=4x+33 x plus 4 equals 4 x plus 34x+3=3x+34 x plus 3 equals 3 x plus 33x+4=3x+33 x plus 4 equals 3 x plus 3
9 answers
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?(1 point)Responses3x+4=3x+43 x plus 4 equals 3 x plus 44x+3=4x+34 x plus 3 equals 4 x plus 33x+4=3x+33 x plus 4 equals 3 x plus 33x+4=4x+33 x plus 4 equals 4 x plus 3
3x+4=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 (1 point)ResponsesThe equation has no solution.The equation has no solution.The equation has one solution: x=3.The equation has one solution: x equals 3 .The equation has one solution: x=−3.The equation has one solution: x equals negative 3 .The equation has infinite solutions.
Let's solve the equation step by step:
3(x+2) - 6 = 3x
Distribute the 3 on the left side:
3x + 6 - 6 = 3x
Combine like terms:
3x = 3x
Subtract 3x from both sides:
0 = 0
Since 0 is equal to 0, this means that the equation has infinite solutions.
3(x+2) - 6 = 3x
Distribute the 3 on the left side:
3x + 6 - 6 = 3x
Combine like terms:
3x = 3x
Subtract 3x from both sides:
0 = 0
Since 0 is equal to 0, this means that the equation has infinite solutions.
Solve for x to determine if the equation has one, none, or infinite solutions. 4x=3(x+5)−15 (1 point)ResponsesThe equation has infinite solutions.The equation has infinite solutions.The equation has no solution.The equation has no solution.The equation has one solution: x=0.The equation has one solution: x equals 0 .The equation has one solution: x=−10.
Let's solve the equation step by step:
4x = 3(x+5) - 15
Distribute the 3 on the right side:
4x = 3x + 15 - 15
Simplify:
4x = 3x
Subtract 3x from both sides:
x = 0
Since x simplifies to a single value (x = 0), this means that the equation has one solution.
4x = 3(x+5) - 15
Distribute the 3 on the right side:
4x = 3x + 15 - 15
Simplify:
4x = 3x
Subtract 3x from both sides:
x = 0
Since x simplifies to a single value (x = 0), this means that the equation has one solution.
Solve for x to determine if the equation has one, none, or infinite solutions. 5(2x+2)−7x=3x+6 (1 point)ResponsesThe equation has one solution: x=6.The equation has one solution: x equals 6 .The equation has infinite solutions.The equation has infinite solutions.The equation has no solution.The equation has no solution.The equation has one solution: x=10.The equation has one solution: x equals 10 .
Let's solve the equation step by step:
5(2x+2) - 7x = 3x + 6
Distribute the 5 on the left side:
10x + 10 - 7x = 3x + 6
Combine like terms:
3x + 10 = 3x + 6
Subtract 3x from both sides:
10 = 6
This equation is not true, as 10 is not equal to 6. So, there are no solutions to this equation.
5(2x+2) - 7x = 3x + 6
Distribute the 5 on the left side:
10x + 10 - 7x = 3x + 6
Combine like terms:
3x + 10 = 3x + 6
Subtract 3x from both sides:
10 = 6
This equation is not true, as 10 is not equal to 6. So, there are no solutions to this equation.