3. Tell whether each equation has one solution, infinitely many solutions, or no solution. (3 points)
6x + 8 = 6(x + 2)
10x = 15 + 5x
x + 11 = 8x + 11 - 7x
Pls, help I really can't figure this out!!!!!!!!!
6x + 8 = 6(x + 2)
6x+8 = 6x+12
8 = 12
In other words, there is no value of x which makes this true. No solution
Try the others, seeing whether x has a value, or whether any x will work.
7-3w=-4w
To determine the number of solutions for each equation, we need to simplify and analyze them one by one:
1. 6x + 8 = 6(x + 2)
Let's simplify the equation:
6x + 8 = 6x + 12
Next, we can subtract 6x from both sides:
8 = 12
Since the resulting statement, 8 = 12, is false, this equation has no solution.
2. 10x = 15 + 5x
First, simplify the equation:
10x = 15 + 5x
Now, subtract 5x from both sides to isolate the x term:
10x - 5x = 15
Combine similar terms on the left side:
5x = 15
Divide both sides by 5:
x = 3
In this case, there is exactly one solution, which is x = 3.
3. x + 11 = 8x + 11 - 7x
Begin by simplifying the equation:
x + 11 = 8x + 11 - 7x
Combine similar terms on the right side:
x + 11 = x + 11
Subtract x from both sides to isolate the x term:
11 = 11
Since 11 = 11 is true, this equation has infinitely many solutions.
To determine whether each equation has one solution, infinitely many solutions, or no solution, we need to simplify and solve each equation. Let's go through each equation step by step:
Equation 1:
6x + 8 = 6(x + 2)
First, distribute the 6 on the right side of the equation:
6x + 8 = 6x + 12
Next, subtract 6x from both sides to simplify:
8 = 12
Since the equation simplifies to a false statement (8 is not equal to 12), there is no solution to this equation.
Equation 2:
10x = 15 + 5x
Combine like terms on the right side of the equation:
10x = 20x
Next, subtract 5x from both sides to simplify:
5x = 0
Divide both sides by 5 to solve for x:
x = 0
Since there is a definite value for x (x = 0), this equation has one solution.
Equation 3:
x + 11 = 8x + 11 - 7x
Combine like terms on the right side of the equation:
x + 11 = x + 11
Next, subtract x from both sides to simplify:
11 = 11
Since the equation simplifies to a true statement (11 is equal to 11), the variable x cancels out. This means that any value plugged into the equation will satisfy it. Therefore, this equation has infinitely many solutions.
To summarize:
- Equation 1 has no solution.
- Equation 2 has one solution (x = 0).
- Equation 3 has infinitely many solutions.