Let's solve the equation \(-7x + 10 = 15 - 7x - 5\).

1. Simplify both sides of the equation:

\[
-7x + 10 = 15 - 7x - 5
\]

The right side simplifies to:

\[
15 - 5 - 7x = 10 - 7x
\]

So the equation becomes:

\[
-7x + 10 = 10 - 7x
\]

2. Now, we can add \(7x\) to both sides of the equation to eliminate the \(-7x\) terms:

\[
-7x + 7x + 10 = 10 - 7x + 7x
\]

This simplifies to:

\[
10 = 10
\]

Since both sides of the equation are equal and no variable remains, this means that the original equation is **true for all values of \(x\)**. 

Therefore, the solution is that **any value of \(x\) will satisfy the equation**. In other words, the solution set is all real numbers (\(\mathbb{R}\)).

Would you like any further details, or do you have any questions?

Here are some related questions to explore:
1. What happens if the coefficients of \(x\) were different on each side?
2. How can we determine if an equation has no solution?
3. What are the steps to solve equations with variables on both sides?
4. How do we solve equations involving absolute values?
5. How can we verify the solution to a linear equation?

**Tip:** When an equation simplifies to a true statement like \(10 = 10\), it indicates that the equation is an identity, meaning it holds for all possible values of the variable.

Learn how to solve the linear equation -7x + 10 = 15 - 7x - 5 with a detailed step-by-step solution. This problem covers solving linear equations and the process of eliminating variables on both sides. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation