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2 answers:
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Answer:
A. 2x = 3x - x
E. x - 1 = 2x - (x + 1)
Step-by-step explanation:
To find out which linear equations have an infinitely many solutions, we must solve for the value of x:
A. 2x = 3x - x
Subtract 2x from both sides:
2x - 2x = 3x - x - 2x
0 = 3x - 3x
0 = 0 This is a true statement, which implies that any values of x will satisfy the given equation. Therefore, this linear equation has infinitely many solutions.
B. 3x = 3(2 + x)
Distribute 3 into (2 + x):
3x = 6 + 3x
Subtract 3x from both sides:
3x - 3x = 6 + 3x - 3x
0 = 6 This is a false statement. Therefore, there is no solution.
C. 4x = x + 4
Subtract x from both sides:
4x - x = x - x + 4
3x = 4
Divide both sides by 3:
x = 4/3 This is the solution to the given equation.
D. -2x = -x - 2
Add x to both sides:
-2x + x = -x + x - 2
-x = -2
Divide both sides by -1:
x = 2 This is the solution to the given equation.
E. x - 1 = 2x - (x + 1)
Distribute -1 into (x + 1):
x - 1 = 2x - x - 1
Add 1 to both sides:
x - 1 + 1 = 2x - x - 1 + 1
x = x
Subtract x from both sides:
x - x = x - x
0 = 0 This is a true statement, which implies that any values of x will satisfy the given equation. Therefore, this linear equation has infinitely many solutions.
Given these calculations, we can see that options A and E have infinitely many solutions.
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