5(x – 9) = 5x

no solution
one solution
infinite solutions

–2(x – 1) = 2x – 2

infinite solutions
one solution
no solution

Anyone?

5(x – 9) = 5x

5x - 45 = 5x
-45 = 0

If your variables drop out and you end up with a true statement, such as 4 = 4, there will be an infinite number of solutions.
If your variables drop out and you end up with a false statement, such as our -45 = 0, there will be no solution.

-2(x-10 = 2x - 2
-2x + 20 = 2x - 2
-4x = -22
x = 11/2, so ... one solution.

Oh. can you help me with one more?

–4 – 5(w + 8)

-5w – 44 ***
–5w + 36
–w – 8
–20w + 8

Am I correct?

correct

Thank you so much! :-)

To determine the number of solutions for each equation, we need to solve them step by step.

1. 5(x – 9) = 5x

First, distribute the 5 on the left side of the equation:
5x - 45 = 5x

Next, subtract 5x from both sides to isolate the variable:
-45 = 0

Since -45 does not equal 0, this equation is inconsistent, meaning there is no solution. The answer is therefore: no solution.

2. –2(x – 1) = 2x – 2

Begin by distributing the -2 on the left side of the equation:
-2x + 2 = 2x - 2

Next, add 2x to both sides to isolate the variable:
2 = 4x - 2

Subsequently, add 2 to both sides to isolate the variable on the right side:
4 = 4x

Lastly, divide both sides by 4 to solve for x:
x = 1

Since x equals 1, this equation has one solution. The answer is therefore: one solution.