Solve for
x
x
.

−
4
(
6
x
−
4
)
=
−
(
4
x
−
6
)
+
30
-
4
(
6
x
-
4
)
=
-
(
4
x
-
6
)
+
30

x
=
x
=

To solve the equation:

\[
-4(6x - 4) = -(4x - 6) + 30
\]

Let's follow the steps to find \( x \).

### Step 1: Expand both sides
First, expand both sides of the equation.

\[
-4(6x - 4) = -4(6x) + (-4)(-4) = -24x + 16
\]
\[
-(4x - 6) = -4x + 6
\]

So the equation becomes:

\[
-24x + 16 = -4x + 6 + 30
\]

### Step 2: Simplify the right-hand side
Now, simplify the right-hand side by combining like terms:

\[
-24x + 16 = -4x + 36
\]

### Step 3: Move all terms involving \( x \) to one side
Add \( 24x \) to both sides to move the \( x \)-terms to one side:

\[
16 = 20x + 36
\]

### Step 4: Isolate the \( x \)-term
Subtract 36 from both sides to isolate the term with \( x \):

\[
16 - 36 = 20x
\]
\[
-20 = 20x
\]

### Step 5: Solve for \( x \)
Now, divide both sides by 20:

\[
x = \frac{-20}{20} = -1
\]

### Final Answer:
\[
x = -1
\]

Would you like further details on any of the steps or have any questions?

---

Here are 5 related questions for further practice:
1. Solve for \( x \): \( 3(2x - 5) = 2(x + 6) \)
2. Solve for \( x \): \( -5(3x + 1) = 15x - 10 \)
3. Solve \( 7x - 4(2x + 5) = -3 \)
4. Solve \( 2(5x + 3) = x + 17 \)
5. Solve \( 6x + 3 = 2(3x - 5) + 13 \)

**Tip**: Always distribute multiplication before combining like terms in equations for easier solving.

Learn how to solve the linear equation -4(6x - 4) = -(4x - 6) + 30 with step-by-step guidance. This problem focuses on key algebraic concepts such as the distributive property and solving for x. Ideal for students in Grades 8-10.

Math Problem Statement

− 4 ( 6 x − 4 )

− ( 4 x − 6 ) + 30

4 ( 6 x

4 )

( 4 x

x

x

Solution

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