A). The equation has one solution: x=−3.
B). The equation has one solution: x=3.
C). The equation has no solution.
D). The equation has infinite solutions.
5 answers
To solve the equation \( 3(x + 2) - 6 = 3x \), let's simplify it step by step.
Distribute the \( 3 \): \[ 3x + 6 - 6 = 3x \] This simplifies to: \[ 3x = 3x \]
Now, subtract \( 3x \) from both sides: \[ 3x - 3x = 3x - 3x \] This simplifies to: \[ 0 = 0 \]
Since the equation simplifies to \( 0 = 0 \), it is always true regardless of the value of \( x \).
Thus, the equation has infinite solutions.
The correct answer is: D). The equation has infinite solutions.
To solve the equation \( 4x = 3(x + 5) - 15 \), let's simplify it step by step.
Distribute the \( 3 \) on the right side: \[ 4x = 3x + 15 - 15 \] This simplifies to: \[ 4x = 3x \]
Now, subtract \( 3x \) from both sides: \[ 4x - 3x = 3x - 3x \] This simplifies to: \[ x = 0 \]
Since we found a specific value for \( x \) (which is \( 0 \)), this equation has one solution.
The correct answer is: C). The equation has one solution: x = 0.
To solve the equation \( 5(2x + 2) - 7x = 3x + 6 \), we will simplify it step by step.
Start by distributing the \( 5 \) on the left side: \[ 10x + 10 - 7x = 3x + 6 \]
Combine like terms on the left: \[ (10x - 7x) + 10 = 3x + 6 \] This simplifies to: \[ 3x + 10 = 3x + 6 \]
Next, subtract \( 3x \) from both sides: \[ 10 = 6 \]
The statement \( 10 = 6 \) is false, indicating that there are no values of \( x \) that satisfy the original equation.
Thus, the equation has no solution.
The correct answer is: C). The equation has no solution.
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