https://file.aiquickdraw.com/mathbot/file/1725652518936w36l2dgs.jpg

The equation in the image appears to be:

\[
\frac{x}{7} + \frac{x - 2}{3} = (x + 1) - 5
\]

Let's solve this equation step by step.

### Step 1: Simplify the right-hand side of the equation.
\[
(x + 1) - 5 = x - 4
\]
Now the equation becomes:
\[
\frac{x}{7} + \frac{x - 2}{3} = x - 4
\]

### Step 2: Find a common denominator for the fractions on the left-hand side.
The common denominator for \(7\) and \(3\) is \(21\). So, rewrite the fractions:
\[
\frac{x}{7} = \frac{3x}{21}, \quad \frac{x - 2}{3} = \frac{7(x - 2)}{21}
\]
Now, the equation is:
\[
\frac{3x}{21} + \frac{7(x - 2)}{21} = x - 4
\]

### Step 3: Combine the fractions on the left-hand side.
\[
\frac{3x + 7(x - 2)}{21} = x - 4
\]
Expanding the numerator:
\[
3x + 7(x - 2) = 3x + 7x - 14 = 10x - 14
\]
Thus, the equation is now:
\[
\frac{10x - 14}{21} = x - 4
\]

### Step 4: Eliminate the fraction by multiplying both sides by 21.
\[
10x - 14 = 21(x - 4)
\]

### Step 5: Distribute the 21 on the right-hand side.
\[
10x - 14 = 21x - 84
\]

### Step 6: Rearrange the equation to isolate \(x\).
Subtract \(10x\) from both sides:
\[
-14 = 11x - 84
\]
Add 84 to both sides:
\[
70 = 11x
\]
Finally, divide both sides by 11:
\[
x = \frac{70}{11}
\]

### Final Answer:
\[
x = \frac{70}{11}
\]

Would you like further details or have any questions?

Here are 5 related questions to further explore:

1. How do you solve a system of equations involving fractions?
2. What is the process of simplifying complex fractions?
3. How can common denominators be useful in solving equations?
4. What are the strategies for isolating variables in algebraic equations?
5. How does clearing fractions help simplify an equation?

**Tip:** Always check your solutions by substituting the value of the variable back into the original equation.

Solve the equation: \frac{x}{7} + \frac{x - 2}{3} = (x + 1) - 5

This detailed solution explains how to solve the algebraic equation \frac{x}{7} + \frac{x - 2}{3} = (x + 1) - 5 step by step. The problem covers algebraic concepts, such as fractions, common denominators, and linear 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