What is the justification for the step taken from line 2 to line 3?
5 lines of math. The first line has, 3 x plus 9 minus 7 x equals x plus 10 plus x. The second line has, negative 4 x plus 9 equals 2 x plus 10. An arrow pointing from the front of the second line to the front of the third line. The third line has, negative 6 x plus 9 equals 10. The fourth line has, negative 6 x equals 1. The last line has x equals negative StartFraction 1 Over 6 EndFraction.
the subtraction property of equality
the multiplication property of equality
combining like terms on one side of the equation
the distributive property
We’re no strangers to love
You know the rules and so do I
A full commitment’s what I’m thinking of
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I just wanna tell you how I’m feeling
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Your heart’s been aching but you’re too shy to say it
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And if you ask me how I’m feeling
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Never gonna give you up
Never gonna let you down
Never gonna run around and desert you
Never gonna make you cry
Never gonna say goodbye
Never gonna tell a lie and hurt you
The justification for the step taken from line 2 to line 3 is combining like terms on one side of the equation.
In line 2, we have the equation -4x + 9 = 2x + 10. To simplify this equation, we can combine the like terms on each side. On the left side, we have -4x and on the right side, we have 2x. By subtracting 2x from both sides, we can move the variable terms to one side of the equation:
-4x + 9 - 2x = 2x - 2x + 10
Simplifying further, we have:
-6x + 9 = 10
To understand the justification for the step taken from line 2 to line 3, let's break it down:
The equation in line 2 is: -4x + 9 = 2x + 10.
To simplify this equation, we can start by combining like terms on each side. Since we have -4x and 2x on the right side, we can combine them to get -2x. The equation becomes: -4x + 9 = -2x + 10.
Next, to isolate the variable x on one side, we need to eliminate the constants (numbers) from the equation. We can do this by subtracting 9 from both sides of the equation. This step is known as applying the subtraction property of equality. By doing so, the equation becomes: -4x = -2x + 1.
Now, we want to get rid of the -2x term on the right side and have all the x terms on the left side. To achieve this, we subtract -2x from both sides of the equation. This can be done using the subtraction property of equality. The equation becomes: -4x + 2x = 1.
Simplifying further, -4x + 2x is equal to -2x. Thus, the equation now is: -2x = 1.
Finally, to solve for x, we need to get rid of the coefficient -2 in front of x. This can be achieved by dividing both sides of the equation by -2, which is applying the multiplication property of equality. The equation becomes: x = -1/2.
Therefore, the justification for the step taken from line 2 to line 3 is combining like terms on one side of the equation.
It would be easier to understand by using the symbols, for example:
3x + 9 - 7x = x + 10 + x
-4x + 9 = 2x + 10
-1 = 6x then x = -1/6
"x equals negative StartFraction 1 Over 6 EndFraction" See above.
Don't make it harder than it needs to be.