Question

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

\\3x + 9 - 7x = x + 10 + x\\
\\-4x + 9 = 2x + 10\\
\\-6x + 9 = 10\\
\\-6x = 1\\
\\x = -\frac{1}{6}\\

the subtraction property of equality
the multiplication property of equality
combining like terms on one side of the equation
the distributive property

Explanation:

Identify the equations in line 2 and line 3

Using the Linear Equations knowledge point
Line 2:

$$ -4x + 9 = 2x + 10 $$

Line 3:

$$ -6x + 9 = 10 $$

Analyze the algebraic transformation

Using the Properties of Equality knowledge point

$$
LATEXBLOCK0
$$

Match with the given options

Using the Properties of Equality knowledge point
Subtracting \(2x\) from both sides of the equation is justified by the subtraction property of equality.

Answer:

• the subtraction property of equality (Correct answer)
• the multiplication property of equality
• combining like terms on one side of the equation
• the distributive property