4x Using Algebraic Properties Solving the equation $$ 6 x+2(x-1)=30 $$ Given: $$ 6 x+2(x-1)=30 $$ Step 1: $$ 6 x+2 x-2=30 $$ Step 2: $$ 8 x-2=30 $$ Step 3: $$ 8 x-2+2=30+2 $$ Step 4: $$ \frac{8 x}{8}=\frac{32}{8} $$ Step 5: $$ x=4 $$

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UpStudy AI · Accepted Answer

Yes, your step-by-step solution to the equation $$ 6x + 2(x - 1) = 30 $$ is correct. Let's walk through each step in detail to ensure everything is clear:

### **Given Equation:**
$$ 6x + 2(x - 1) = 30 $$

### **Step 1: Apply the Distributive Property**
Distribute the 2 across the terms inside the parentheses.
$$ 6x + 2 \cdot x - 2 \cdot 1 = 30 $$
$$ 6x + 2x - 2 = 30 $$

### **Step 2: Combine Like Terms**
Combine the $$ x $$-terms ($$ 6x $$ and $$ 2x $$).
$$ (6x + 2x) - 2 = 30 $$
$$ 8x - 2 = 30 $$

### **Step 3: Add 2 to Both Sides**
Isolate the term with $$ x $$ by adding 2 to both sides of the equation.
$$ 8x - 2 + 2 = 30 + 2 $$
$$ 8x = 32 $$

### **Step 4: Divide Both Sides by 8**
Solve for $$ x $$ by dividing both sides by 8.
$$ \frac{8x}{8} = \frac{32}{8} $$
$$ x = 4 $$

### **Conclusion:**
$$ x = 4 $$

Your solution correctly applies the distributive property, combines like terms, and isolates the variable $$ x $$ to find that $$ x = 4 $$ is the solution to the equation.

If you have any further questions or need additional explanations on any of the steps, feel free to ask!
$$ x = 4 $$

4x Using Algebraic Properties
Solving the equation
Given:
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:

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Solución

Given Equation:

Step 1: Apply the Distributive Property

Step 2: Combine Like Terms

Step 3: Add 2 to Both Sides

Step 4: Divide Both Sides by 8

Conclusion:

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4x Using Algebraic Properties Solving the equation Given: Step 1: Step 2: Step 3: Step 4: Step 5: