Question

Order the steps for solving the equation: 2x−5=3(4x+5)
Step 1:
Property to get


Step 2:
Property to get

Step 3:
Property to get

Step 4:
Property to get

Answer 1

To solve the equation \( 2x - 5 = 3(4x + 5) \), we can break the process into clear steps. Here’s the ordered sequence of steps to follow, along with the properties used:

**Step 1:** Distribute on the right-hand side.

\[
2x - 5 = 3(4x + 5) \implies 2x - 5 = 12x + 15
\]

**Property used:** Distributive Property

---

**Step 2:** Move the terms involving \( x \) to one side of the equation.

\[
2x - 12x = 15 + 5
\]

This simplifies to:

\[
-10x = 20
\]

**Property used:** Addition Property of Equality (adding \( 12x \) to both sides and adding 5 to both sides)

---

**Step 3:** Isolate \( x \) by dividing both sides by -10.

\[
x = \frac{20}{-10}
\]

This simplifies to:

\[
x = -2
\]

**Property used:** Division Property of Equality

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**Step 4:** Write the final answer.

\[
x = -2
\]

**Property used:** Solution conclusion

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So, the ordered steps are:

1. Distribute on the right-hand side.
2. Move terms involving \( x \) to one side of the equation.
3. Isolate \( x \) by division.
4. Write the final answer.