3x+7\left(x-5\right)=6\left(2x-1\right)-8

We are given the equation:

\[
3x + 7(x - 5) = 6(2x - 1) - 8
\]

Let's solve it step by step.

### Step 1: Expand both sides of the equation
Distribute the constants inside the parentheses on both sides.

- On the left-hand side:
\[
3x + 7(x - 5) = 3x + 7x - 35 = 10x - 35
\]

- On the right-hand side:
\[
6(2x - 1) - 8 = 12x - 6 - 8 = 12x - 14
\]

So the equation becomes:
\[
10x - 35 = 12x - 14
\]

### Step 2: Move all terms involving \(x\) to one side and constants to the other
Subtract \(10x\) from both sides:
\[
-35 = 2x - 14
\]

### Step 3: Solve for \(x\)
Add 14 to both sides:
\[
-35 + 14 = 2x
\]
\[
-21 = 2x
\]

Now divide both sides by 2:
\[
x = \frac{-21}{2}
\]

Thus, the solution is:
\[
x = -\frac{21}{2} \quad \text{or} \quad x = -10.5
\]

Would you like a detailed explanation on any step or have further questions?

Here are 5 related questions:
1. How would the solution change if we alter the constants in the equation?
2. What is the importance of distributing correctly when solving equations like this?
3. Can you solve a similar equation: \(4x + 2(x + 3) = 5(2x - 4)\)?
4. How do we check the solution to ensure it is correct?
5. How does solving linear equations relate to solving systems of equations?

**Tip:** Always check your final solution by substituting it back into the original equation.

Learn how to solve the linear equation 3x + 7(x - 5) = 6(2x - 1) - 8 with a detailed step-by-step solution. This problem involves the distributive property and moving terms to isolate the variable. Ideal for students in Grades 7-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation