3(x+2)−6=3x
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5 answers
To solve the equation \( 3(x + 2) - 6 = 3x \), we will first simplify the left side.
Distribute the \( 3 \) into \( (x + 2) \): \[ 3x + 6 - 6 = 3x \]
Simplify the left side: \[ 3x + 6 - 6 = 3x \implies 3x = 3x \]
Now, we have: \[ 3x = 3x \]
This equation is always true, meaning it holds for any value of \( x \).
Since the equation is true for all values of \( x \), we conclude that the equation has infinite solutions.
To solve the equation \( 4x = 3(x + 5) - 15 \), we'll start by simplifying the right side.
Distribute the \( 3 \) on the right side: \[ 4x = 3x + 15 - 15 \]
Simplify the right side: \[ 4x = 3x + 0 \implies 4x = 3x \]
Next, we can subtract \( 3x \) from both sides: \[ 4x - 3x = 0 \implies x = 0 \]
Now we have found a specific solution, \( x = 0 \).
Thus, there is one solution to the equation.
To solve the equation \( 5(2x + 2) - 7x = 3x + 6 \), we start by simplifying both sides.
Distribute the \( 5 \) on the left side: \[ 10x + 10 - 7x = 3x + 6 \]
Combine like terms on the left side: \[ (10x - 7x) + 10 = 3x + 6 \implies 3x + 10 = 3x + 6 \]
Now we can isolate the terms involving \( x \): \[ 3x + 10 - 3x = 6 \implies 10 = 6 \]
The statement \( 10 = 6 \) is false, which means that there is no solution to the equation.
Therefore, the equation has no solutions.
