Solve
−
8
(
x
−
1
)
+
8
=
−
5
(
x
−
2
)
-
8
(
x
-
1
)
+
8
=
-
5
(
x
-
2
)
for
x
x

x
=

Let's solve the equation:

\[
-8(x - 1) + 8 = -5(x - 2)
\]

### Step 1: Distribute the constants.
Distribute \(-8\) on the left-hand side and \(-5\) on the right-hand side.

\[
-8(x - 1) = -8x + 8
\quad \text{so,} \quad -8(x - 1) + 8 = -8x + 8 + 8 = -8x + 16
\]

\[
-5(x - 2) = -5x + 10
\]

Now, the equation is:

\[
-8x + 16 = -5x + 10
\]

### Step 2: Bring all terms involving \(x\) to one side.
Move \(-5x\) to the left-hand side and the constant terms to the right-hand side.

\[
-8x + 5x = 10 - 16
\]

\[
-3x = -6
\]

### Step 3: Solve for \(x\).
Now, divide both sides by \(-3\):

\[
x = \frac{-6}{-3} = 2
\]

### Final Answer:
\[
x = 2
\]

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

Here are 5 related questions for practice:
1. Solve \( 5(x + 4) - 3 = 7(x - 2) + 6 \) for \(x\).
2. Solve \( 4 - 2(x + 1) = -6 + 3(x - 3) \) for \(x\).
3. What is the solution to \( 7(x - 5) = 3(x + 1) + 2(x - 3) \)?
4. Solve the equation \( 10 - 2(3x + 1) = 4x - 8 \).
5. How do you solve \( -6(x - 4) + 3 = 12(x + 2) \)?

**Tip**: Always remember to simplify both sides of an equation by distributing constants and combining like terms first before solving for the variable.

Learn how to solve the linear equation -8(x - 1) + 8 = -5(x - 2) for x with step-by-step guidance. This algebraic problem covers key concepts such as the distributive property and solving linear equations. Ideal for students in Grades 7-9.

Math Problem Statement

Solve − 8 ( x − 1 ) + 8

− 5 ( x − 2 )

8 ( x

1 ) + 8

5 ( x

x

Solution

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