Divide[2x-3,15]-Divide[x+4,3]=Divide[7x-1,15]

We are given the equation:

\[
\frac{2x - 3}{15} - \frac{x + 4}{3} = \frac{7x - 1}{15}
\]

Let's solve it step by step.

### Step 1: Find a common denominator

We have denominators of 15 and 3, so the common denominator between these is 15. Rewrite the second term so that its denominator is 15:

\[
\frac{2x - 3}{15} - \frac{x + 4}{3} = \frac{7x - 1}{15}
\]

Multiply the numerator and denominator of the second term by 5 to get a denominator of 15:

\[
\frac{2x - 3}{15} - \frac{5(x + 4)}{15} = \frac{7x - 1}{15}
\]

This becomes:

\[
\frac{2x - 3}{15} - \frac{5(x + 4)}{15} = \frac{7x - 1}{15}
\]

### Step 2: Combine the fractions on the left-hand side

Since both fractions on the left-hand side have the same denominator, we can combine them:

\[
\frac{(2x - 3) - 5(x + 4)}{15} = \frac{7x - 1}{15}
\]

Simplify the expression in the numerator:

\[
(2x - 3) - 5(x + 4) = 2x - 3 - 5x - 20 = -3x - 23
\]

So the equation becomes:

\[
\frac{-3x - 23}{15} = \frac{7x - 1}{15}
\]

### Step 3: Eliminate the denominator

Since both sides have the same denominator, we can eliminate it by multiplying both sides of the equation by 15:

\[
-3x - 23 = 7x - 1
\]

### Step 4: Solve for \(x\)

Now, solve the equation:

\[
-3x - 23 = 7x - 1
\]

Add \(3x\) to both sides:

\[
-23 = 10x - 1
\]

Add 1 to both sides:

\[
-22 = 10x
\]

Now, divide both sides by 10:

\[
x = \frac{-22}{10} = -\frac{11}{5}
\]

### Final Answer:

\[
x = -\frac{11}{5}
\]

Would you like further details or explanations on any of these steps?

Here are 5 questions to further explore the concept:
1. How do you handle equations with different denominators?
2. What are common techniques for simplifying algebraic fractions?
3. How do you verify a solution after solving an equation?
4. Can an equation have more than one solution in some cases?
5. What is the significance of common denominators in algebra?

**Tip:** Always check your solution by plugging the value back into the original equation to ensure it satisfies both sides.

Explore the detailed steps to solve the algebraic equation with fractions: Divide[2x-3,15]-Divide[x+4,3]=Divide[7x-1,15]. This problem involves key algebraic concepts such as finding a common denominator and simplifying expressions. Suitable for students in Grades 8-10.

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