Linear equation: -1

Question

2
(6x + 10) = 13

Step 1: –3x – 5 = 13

Step 2: –3x = 18

Step 3: x = –6

Which sequence describes the inverse operations used for steps 2 and 3 to solve the linear equation?
the addition property of equality and then the division property of equality
the addition property of equality and then the multiplication property of equality
the subtraction property of equality and then the division property of equality
the subtraction property of equality and then the multiplication property of equality

Answer 1

To solve the equation in your steps:

Step 1: \(-3x - 5 = 13\)

In Step 2, you isolate the term involving \(x\) by adding \(5\) to both sides, which is the addition property of equality:

\[ -3x - 5 + 5 = 13 + 5 \] This simplifies to: \[ -3x = 18 \]

In Step 3, you solve for \(x\) by dividing both sides by \(-3\), which is the division property of equality:

\[ x = \frac{18}{-3} \] This simplifies to: \[ x = -6 \]

Thus, the sequence of inverse operations used for steps 2 and 3 is:

the addition property of equality and then the division property of equality.