Question

the following table shows the steps involved in solving a linear equation. which of the following properties correctly fills in the missing step used to get the equation in its corresponding form?

equation	steps
?	addition property of equality
$x + 6 = \frac{13}{7}$	division property of equality
$x = -\frac{29}{7}$	subtraction property of equality

show your work here

$\circ$ $x + 6 - 7 = 13$ $\circ$ $7(x + 6) = 13$
$\circ$ $x + 6 + 7 = 13$ $\circ$ $\frac{x + 6}{7} = 13$

Explanation:

Step1: Analyze the original equation

The original equation is \(7(x + 6)-4 = 9\). We need to use the addition property of equality, which means we add the same number to both sides of the equation.

Step2: Apply the addition property of equality

To isolate the term with the parentheses, we add 4 to both sides of the equation \(7(x + 6)-4 = 9\).
Adding 4 to both sides: \(7(x + 6)-4+4=9 + 4\).
Simplifying both sides, we get \(7(x + 6)=13\).

Answer:

\(7(x + 6)=13\) (the option with this equation)