1. 2(x – 3) = 2x
one solution
no solutions
infinitely many solutions
2. 3(y – 3) = 2y – 9 + y
one solution
no solutions
infinitely many solutions
3. 10x – 2 – 6x = 3x – 2 + x
one solution
no solutions
infinitely many solutions
4. 4(x + 3) + 2x = x – 8
one solution
no solutions
infinitely many solutions
HELP????
and your answers are? I will be happy to check them.
B
C
C
A
@bobpursley
all correct
Yes, I knew it! Thank you @bobpursley
To find the solutions to these equations, we can simplify and solve each equation step by step.
1. 2(x – 3) = 2x
Expand the brackets:
2x - 6 = 2x
Subtract 2x from both sides:
-6 = 0
The equation -6 = 0 is not true, so the equation has no solutions.
2. 3(y – 3) = 2y – 9 + y
Expand the brackets:
3y - 9 = 2y - 9 + y
Combine like terms:
3y - 9 = 3y - 9
Subtract 3y from both sides:
-9 = -9
The equation -9 = -9 is true, so the equation has infinitely many solutions. Any value of y will satisfy the equation.
3. 10x – 2 – 6x = 3x – 2 + x
Combine like terms:
4x - 2 = 4x - 2
Subtract 4x from both sides:
-2 = -2
The equation -2 = -2 is true, so the equation has infinitely many solutions. Any value of x will satisfy the equation.
4. 4(x + 3) + 2x = x – 8
Distribute the 4:
4x + 12 + 2x = x - 8
Combine like terms:
6x + 12 = x - 8
Subtract x and 12 from both sides:
5x = -20
Divide by 5:
x = -4
The equation has one solution, x = -4.
In summary, the answers to the equations are:
1. No solutions
2. Infinitely many solutions
3. Infinitely many solutions
4. One solution, x = -4