decide whether each equation has one solution, no solution, or infinitely many solutions.
1. 2(x-3) = 2x
2. 3(y-3) = 2y-9+y
3. 10x-2-6x=3x-2+x
4. 4(x+3) = 2x= x-8
please be quick!!
simplify each equation, each of which is linear.
If your variable drops out, and
you get a true statement ----> an infinite number of solutions
you get a false statement ---> no solution
If you end up with the variable remaining in the equation, you will have
one solution
e.g. the first one:
2(x-3) = 2x
2x - 6 = 2x
subtract 2x from both sides:
-6 = 0 , which is false, so.... no solution
do the rest in the same way.
btw, you have a typo in the last, two equal signs.
4. 4(x+3) + 2x = x-8
thx mathhelper
To determine the number of solutions for each equation, we need to simplify and solve the equations. Let's go through each one:
1. 2(x-3) = 2x
Start by distributing the 2 on the left side:
2x - 6 = 2x
Combine like terms:
-6 = 0
The equation simplifies to -6 = 0. This is not a true statement since -6 does not equal 0. Therefore, there is no solution for this equation.
2. 3(y-3) = 2y-9+y
Start by distributing the 3 on the left side:
3y - 9 = 2y - 9 + y
Combine like terms:
3y - 9 = 3y - 9
The variables completely cancel out, and we are left with -9 = -9. This is a true statement since -9 does equal -9. Therefore, this equation has infinitely many solutions.
3. 10x - 2 - 6x = 3x - 2 + x
Combine like terms on both sides:
4x - 2 = 4x - 2
The variables completely cancel out, and we are left with -2 = -2. This is a true statement since -2 does equal -2. Therefore, this equation has infinitely many solutions.
4. 4(x+3) = 2x = x - 8
There might be a mistake in the equation since there is an extra equal sign. Assuming you meant 4(x+3) = 2x + x - 8, we can solve it.
Start by distributing the 4 on the left side:
4x + 12 = 2x + x - 8
Combine like terms:
4x + 12 = 3x - 8
Subtract 3x from both sides:
x + 12 = -8
Subtract 12 from both sides:
x = -20
The equation simplifies to x = -20. This is a single solution, so there is one solution for this equation.
To summarize:
1. No solution
2. Infinitely many solutions
3. Infinitely many solutions
4. One solution (x = -20)