x
+
1
5
=
−
4
(
2
3
x
+
4
)
1
4
x
+
1
5
=
-
4
(
2
3
x
+
4
)

You have the following equation:

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

Let me walk through solving it step by step.

### Step 1: Distribute the \(-4\) on the right-hand side.

\[
\frac{1}{5}x + \frac{1}{5} = -4 \times \frac{2}{3}x - 4 \times 4
\]

Simplifying the right-hand side:

\[
\frac{1}{5}x + \frac{1}{5} = -\frac{8}{3}x - 16
\]

### Step 2: Eliminate the fractions by multiplying the entire equation by the least common denominator (LCD) of 5 and 3, which is 15.

Multiplying each term by 15:

\[
15\left(\frac{1}{5}x\right) + 15\left(\frac{1}{5}\right) = 15\left(-\frac{8}{3}x - 16\right)
\]

This simplifies to:

\[
3x + 3 = -40x - 240
\]

### Step 3: Combine like terms by adding \(40x\) to both sides and subtracting 3 from both sides.

\[
3x + 40x = -240 - 3
\]

\[
43x = -243
\]

### Step 4: Solve for \(x\) by dividing both sides by 43.

\[
x = \frac{-243}{43}
\]

Thus, the solution is:

\[
x = \frac{-243}{43}
\]

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

---

Here are 5 related questions:
1. What is the process for solving equations with fractions?
2. How do you find the least common denominator (LCD)?
3. How do you simplify algebraic expressions with distributive properties?
4. How do you check the solution of an equation?
5. What is the best way to handle negative signs when solving equations?

**Tip:** Always multiply through by the least common denominator when working with fractions to simplify the equation early in the process.

Learn how to solve the linear equation 1/5x + 1/5 = -4(2/3x + 4) with a detailed step-by-step explanation. This problem involves solving linear equations, working with fractions, and applying the distributive property. Suitable for students in Grades 8-10.

Math Problem Statement

x + 1 5

− 4 ( 2 3 x + 4 ) 1 4 x + 1 5

Solution

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