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What is the justification for the step taken from line 2 to line 3?

[tex]\[
\begin{aligned}
3x + 9 - 7x &= x + 10 + x \\
-4x + 9 &= 2x - 10 \\
-6x + 9 &= -10 \\
-6x &= -19 \\
x &= \frac{19}{6}
\end{aligned}
\][/tex]

A. the subtraction property of equality
B. the multiplication property of equality
C. combining like terms on one side of the equation
D. the distributive property

Sagot :

GinnyAnswer
The justification for the step taken from line 2 to line 3 is:

Combining like terms on one side of the equation.

Let's detail each step:

Starting with the equation:
[tex]\[ 3x + 9 - 7x = x + 10 + x \][/tex]

First, we combine like terms on each side of the equation:

On the left side:
[tex]\[ 3x - 7x + 9 = -4x + 9 \][/tex]

On the right side:
[tex]\[ x + x + 10 = 2x + 10 \][/tex]

Putting it together we get:
[tex]\[ -4x + 9 = 2x + 10 \][/tex]

So, the correct justification for the step from:
[tex]\[ 3x + 9 - 7x = x + 10 + x \][/tex]
to:
[tex]\[ -4x + 9 = 2x + 10 \][/tex]

is combining like terms on one side of the equation.
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