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 + 5


Step 2:
Combine Like Terms
Property to get
2x = 12x + 10

Step 3:
Property to get

Step 4:
Property to get

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Answer 1

To solve the equation \(2x - 5 = 3(4x + 5)\), let's outline the steps in order and fill in the necessary information.

Step 1: Distributive Property

Start by applying the distributive property on the right side of the equation:

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

This becomes:

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

Step 2: Combine Like Terms

Next, we want to get all the terms involving \(x\) on one side and constant terms on the other. We can subtract \(12x\) from both sides:

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

This simplifies to:

\[ -10x - 5 = 15 \]

Step 3: Isolate the Variable

Now, add \(5\) to both sides to isolate the term with \(x\):

\[ -10x = 15 + 5 \]

This simplifies to:

\[ -10x = 20 \]

Step 4: Solve for the Variable

Finally, divide by \(-10\) to solve for \(x\):

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

This gives:

\[ x = -2 \]

So to summarize, here are the ordered steps for solving the equation:

1. Distributive Property: Expand the equation to get \(2x - 5 = 12x + 15\).
2. Combine Like Terms: Rearrange the equation to get \(-10x - 5 = 15\).
3. Isolate the Variable: Add \(5\) to both sides to obtain \(-10x = 20\).
4. Solve for the Variable: Divide by \(-10\) to find \(x = -2\).