6
(
x
+
8
)
+
4
=
−
11
(
x
−
1
)
−
2
6
(
x
+
8
)
+
4
=
-
11
(
x
-
1
)
-
2

x
=

Let's solve the equation step by step:

Given equation:
\[
6(x + 8) + 4 = -11(x - 1) - 2
\]

### Step 1: Distribute the constants on both sides.
Distribute the \(6\) on the left-hand side and the \(-11\) on the right-hand side:
\[
6x + 48 + 4 = -11x + 11 - 2
\]

### Step 2: Simplify both sides.
Combine like terms on both sides:
\[
6x + 52 = -11x + 9
\]

### Step 3: Move all terms involving \(x\) to one side.
Add \(11x\) to both sides:
\[
6x + 11x + 52 = 9
\]
\[
17x + 52 = 9
\]

### Step 4: Move constant terms to the other side.
Subtract \(52\) from both sides:
\[
17x = 9 - 52
\]
\[
17x = -43
\]

### Step 5: Solve for \(x\).
Divide both sides by 17:
\[
x = \frac{-43}{17}
\]

So, the solution is:
\[
x = -\frac{43}{17}
\]

Would you like any further clarification or details on this solution?

Here are 5 related questions:
1. How do you handle equations with multiple variables?
2. What happens when there are no solutions to an equation?
3. Can you always solve linear equations using the same method?
4. How do you solve quadratic equations differently from linear ones?
5. What does it mean when an equation has an infinite number of solutions?

**Tip**: Always double-check your distribution step to avoid mistakes in solving complex equations!

Learn how to solve the linear equation 6(x + 8) + 4 = -11(x - 1) - 2 with a detailed step-by-step breakdown. This solution covers key algebraic concepts such as the distributive property and isolating variables. Suitable for students in Grades 8-10.

Math Problem Statement

6 ( x + 8 ) + 4

− 11 ( x − 1 ) − 2 6 ( x + 8 ) + 4

11 ( x

1 )

x

Solution

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