Question
Order the steps for solving the equation: 2x−5=3(4x+5)
(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
Step 3:
Property to get
Step 4:
Property to get
Skip to navigation
page 6 of 6
(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
Step 3:
Property to get
Step 4:
Property to get
Skip to navigation
page 6 of 6
Answers
GPT-4o mini
To solve the equation \( 2x−5=3(4x+5) \), we can follow these steps:
1. **Step 1: Distributive Property**
\[
2x - 5 = 3(4x + 5) \implies 2x - 5 = 12x + 15
\]
2. **Step 2: Combine Like Terms**
To get all the \( x \) terms on one side and constant terms on the other side, we can rearrange the equation:
\[
2x - 12x = 15 + 5 \implies -10x = 20
\]
3. **Step 3: Solve for x**
Now, divide both sides by -10:
\[
x = \frac{20}{-10} \implies x = -2
\]
4. **Step 4: Check the Solution**
Substitute \( x = -2 \) back into the original equation to ensure it holds:
\[
2(-2) - 5 = 3(4(-2) + 5) \implies -4 - 5 = 3(-8 + 5) \implies -9 = 3(-3) \implies -9 = -9
\]
The equation is satisfied.
So the ordered steps are:
1. Distributive Property to get: \( 2x - 5 = 12x + 15 \)
2. Combine Like Terms to get: \( -10x = 20 \)
3. Solve for \( x \) to get: \( x = -2 \)
4. Check the solution to verify the result.
1. **Step 1: Distributive Property**
\[
2x - 5 = 3(4x + 5) \implies 2x - 5 = 12x + 15
\]
2. **Step 2: Combine Like Terms**
To get all the \( x \) terms on one side and constant terms on the other side, we can rearrange the equation:
\[
2x - 12x = 15 + 5 \implies -10x = 20
\]
3. **Step 3: Solve for x**
Now, divide both sides by -10:
\[
x = \frac{20}{-10} \implies x = -2
\]
4. **Step 4: Check the Solution**
Substitute \( x = -2 \) back into the original equation to ensure it holds:
\[
2(-2) - 5 = 3(4(-2) + 5) \implies -4 - 5 = 3(-8 + 5) \implies -9 = 3(-3) \implies -9 = -9
\]
The equation is satisfied.
So the ordered steps are:
1. Distributive Property to get: \( 2x - 5 = 12x + 15 \)
2. Combine Like Terms to get: \( -10x = 20 \)
3. Solve for \( x \) to get: \( x = -2 \)
4. Check the solution to verify the result.