Sure! Here’s a challenging linear equation for you:

\( 7x - 3(2x - 4) + 5 = 2(4x + 1) - 9 \)

Would you like to solve it as well?

Let's solve the linear equation step by step:

The equation is:
\[
7x - 3(2x - 4) + 5 = 2(4x + 1) - 9
\]

### Step 1: Expand both sides
Distribute the terms inside the parentheses on both sides.

Left-hand side:
\[
7x - 3(2x - 4) + 5 = 7x - 6x + 12 + 5
\]
Simplify:
\[
7x - 6x + 12 + 5 = x + 17
\]

Right-hand side:
\[
2(4x + 1) - 9 = 8x + 2 - 9
\]
Simplify:
\[
8x - 7
\]

So, the equation becomes:
\[
x + 17 = 8x - 7
\]

### Step 2: Move all the \( x \)-terms to one side and the constants to the other side
Subtract \( x \) from both sides:
\[
17 = 7x - 7
\]
Now add 7 to both sides:
\[
24 = 7x
\]

### Step 3: Solve for \( x \)
Divide both sides by 7:
\[
x = \frac{24}{7}
\]

Thus, the solution is:
\[
x = \frac{24}{7}
\]

Let me know if you'd like further details or clarifications!

---

Here are 5 related questions:
1. How can we check if \( x = \frac{24}{7} \) is the correct solution?
2. Can we solve this equation using a graphical method?
3. What if the equation had fractions? How would the steps differ?
4. How do we interpret the solution of a linear equation on a number line?
5. What happens if both sides of the equation simplify to the same expression?

**Tip:** Always simplify both sides of the equation first before isolating the variable!

Sure! Here’s a challenging linear equation for you: 7x - 3(2x - 4) + 5 = 2(4x + 1) - 9. Would you like to solve it as well?

Learn how to solve the linear equation 7x - 3(2x - 4) + 5 = 2(4x + 1) - 9 with a clear step-by-step explanation. This solution covers key algebra concepts, including the distributive property and simplifying equations, suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation