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
?	subtraction property of equality
$40 = x - 3$	multiplication property of equality
$43 = x$	addition property of equality
$x = 43$	symmetric property of equality

show your work here
\\(\bigcirc\\) $5 = \frac{x - 3}{8}$ \\(\bigcirc\\) $5 = x - 3 - 8$
\\(\bigcirc\\) $5 = x - 3 + 8$ \\(\bigcirc\\) $5 = 8(x - 3)$

Explanation:

Step1: Recall Subtraction Property

The subtraction property of equality states that if we subtract the same number from both sides of an equation, the equation remains true. The original equation is \(10=\frac{x - 3}{8}+5\). We need to apply the subtraction property, so we subtract 5 from both sides.

Step2: Apply Subtraction to Equation

Subtract 5 from both sides: \(10-5=\frac{x - 3}{8}+5 - 5\). Simplifying the left side gives \(5\), and the right side simplifies to \(\frac{x - 3}{8}\). So the equation becomes \(5=\frac{x - 3}{8}\).

Answer:

\(5=\frac{x - 3}{8}\) (the first option: \(5=\frac{x - 3}{8}\))