https://file.aiquickdraw.com/mathbot/file/1726668111822uz4gi8zq.jpg

The equation provided in the image is:

\[
-\frac{6}{5}(x - 4) = 66
\]

Let's solve this step-by-step.

### Step 1: Eliminate the fraction by multiplying both sides by \( -\frac{5}{6} \):

\[
(x - 4) = 66 \times -\frac{5}{6}
\]

### Step 2: Simplify the right-hand side:

\[
66 \times -\frac{5}{6} = -55
\]

Thus, the equation becomes:

\[
x - 4 = -55
\]

### Step 3: Solve for \( x \):

\[
x = -55 + 4 = -51
\]

So, the solution is:

\[
x = -51
\]

Would you like further clarification or additional details?

Here are some related questions to deepen your understanding:
1. How would you solve this equation if the fraction had a different denominator?
2. What if the sign on \( \frac{6}{5} \) were positive instead of negative?
3. How does multiplying both sides of the equation help simplify the solution?
4. Can you solve a similar equation with variables on both sides?
5. How would this equation change if it were a quadratic equation instead?

**Tip:** Always ensure you simplify fractions and perform the same operation on both sides of an equation to maintain balance!

Learn how to solve the linear equation -(6/5)(x - 4) = 66 with a step-by-step guide. This problem involves simplifying a linear equation with fractions and isolating the variable x, using properties of equality. 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