Solve the equation
−
5
x
=
2
/3
(
3
x
+
6
)
algebraically. Answer as a "reduced Proper or Improper" fraction only.

We are given the equation:

\[
-5x = \frac{2}{3}(3x + 6)
\]

To solve this equation, follow these steps:

### Step 1: Distribute the \(\frac{2}{3}\) on the right-hand side.
\[
\frac{2}{3}(3x + 6) = \frac{2}{3} \cdot 3x + \frac{2}{3} \cdot 6
\]
\[
= 2x + 4
\]

The equation now becomes:
\[
-5x = 2x + 4
\]

### Step 2: Move all terms involving \(x\) to one side of the equation.
Subtract \(2x\) from both sides:
\[
-5x - 2x = 4
\]
\[
-7x = 4
\]

### Step 3: Solve for \(x\).
Divide both sides by \(-7\):
\[
x = \frac{4}{-7}
\]
\[
x = -\frac{4}{7}
\]

Thus, the solution is:
\[
x = -\frac{4}{7}
\]

Would you like further details on this solution or have any questions?

Here are 5 related questions to expand on this:
1. How do you solve equations with different fractions?
2. How can we check if the solution is correct?
3. Can this equation have multiple solutions?
4. How would the solution change if the equation involved exponents?
5. What are the differences between proper and improper fractions?

**Tip:** When dealing with fractions, multiplying out common terms early can simplify the problem.

Solve the equation -5x = 2/3(3x + 6) algebraically. Answer as a 'reduced Proper or Improper' fraction only.

Learn how to solve the linear equation -5x = 2/3(3x + 6) with a detailed step-by-step guide. This solution involves distributing fractions and combining like terms to find x in its reduced form, making it suitable for students in Grades 7-10.

Math Problem Statement

Solve the equation − 5 x

Solution

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