Describe the number of solutions for the equation.
5(x – 9) = 5x
no solution
one solution
infinite solutions
–2(x – 1) = 2x – 2 (1 point)
infinite solutions
one solution
no solution
5x -45 = 5x No
-2x+2 = 2x-2
4 = 4x
What do you think?
I'm late but the first question is b= One solution. hope I helped whoever is looking:)
Let's solve each equation step by step to determine the number of solutions.
1. For the equation 5(x – 9) = 5x:
Distribute 5 to both terms inside the parentheses:
5x - 45 = 5x
Next, subtract 5x from both sides of the equation:
-45 = 0
We end up with the equation -45 = 0, which is not true. This means that the equation has no solution.
Therefore, the number of solutions for the equation 5(x – 9) = 5x is: no solution.
2. For the equation –2(x – 1) = 2x – 2:
Distribute -2 to both terms inside the parentheses:
-2x + 2 = 2x - 2
Next, add 2x to both sides of the equation:
2 = 4x - 2x
Simplify the equation:
2 = 2x
Divide both sides of the equation by 2:
1 = x
We end up with the equation 1 = x, which means that x has a single value of 1.
Therefore, the number of solutions for the equation –2(x – 1) = 2x – 2 is: one solution.
To determine the number of solutions for an equation, we need to simplify and solve the equation. Let's start with the first equation:
5(x – 9) = 5x
To solve this equation, we can distribute the 5 to both terms inside the parentheses:
5x - 45 = 5x
Next, we can subtract 5x from both sides to eliminate the variable on the right side:
-45 = 0
However, this equation leads to a contradiction. -45 does not equal 0. Therefore, there is no value of x that satisfies this equation.
Therefore, the answer is: no solution.
Moving on to the second equation:
–2(x – 1) = 2x – 2
Again, we can distribute the -2 to both terms inside the parentheses:
-2x + 2 = 2x - 2
To solve for x, we can combine like terms by subtracting 2x from both sides:
2 = 4x - 2
Next, we can add 2 to both sides:
4 = 4x
Finally, we can divide both sides by 4 to isolate x:
1 = x
In this case, we end up with a specific value for x, which means there is only one solution.
Therefore, the answer is: one solution.