Order the steps for solving the equation: 2x−5=3(4x+5)

Question

(8 points)
2x−5=3(4x+5)
Step 1:
Distributive
Property to get
2x - 5 = 12x + 15


Step 2:
Addition of Equality
Property to get
2x = 3x + 10

Step 3:
Combine Like Terms
Property to get
-10x = 20

Step 4:
Division of Equality
Property to get
x = -2

Answer 1

To solve the equation $2x-5=3(4x+5)$, we can follow these steps in the correct order:

1. Step 1: Distributive Property to get: $$2x-5=12x+15$$

2. Step 2: Addition of Equality Property to get: $$2x-12x=15+5\text{(adding -12x to both sides and }+5\text{ to both sides)}$$ This simplifies to: $$-10x=20$$

3. Step 3: Division of Equality Property to get: $$x=-2\text{(dividing both sides by -10)}$$

Note that the step where you mentioned "Combine Like Terms" isn't necessary in that way, since once $2x-12x=20$ is simplified directly.

So the correct order of steps should be:

1. Step 1: Distributive Property
2. Step 2: Addition of Equality Property
3. Step 3: Combine Like Terms (which occurs in Step 2) but is implied
4. Step 4: Division of Equality Property

Final ordered steps:

1. Distributive Property to get $2x-5=12x+15$
2. Addition of Equality Property to get $-10x=20$
3. Division of Equality Property to get $x=-2$