How many solutions does this equation have?

9(–3*j* + 15) = 3 − 15*j*

Let's solve the given equation:

\[ 9(-3j + 15) = 3 - 15j \]

### Step 1: Expand both sides of the equation

Expand the left side by distributing the 9:

\[
9(-3j + 15) = 9 \times (-3j) + 9 \times 15
\]

\[
= -27j + 135
\]

So, the equation becomes:

\[
-27j + 135 = 3 - 15j
\]

### Step 2: Move all terms involving \( j \) to one side

Add \( 15j \) to both sides to get all terms with \( j \) on the left:

\[
-27j + 15j + 135 = 3
\]

\[
-12j + 135 = 3
\]

### Step 3: Move constant terms to the other side

Subtract 135 from both sides:

\[
-12j = 3 - 135
\]

\[
-12j = -132
\]

### Step 4: Solve for \( j \)

Divide both sides by \(-12\):

\[
j = \frac{-132}{-12} = 11
\]

### Conclusion:
The equation has **one solution**, which is \( j = 11 \).

Do you want more details or have any questions?

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Here are 5 related questions for practice:

1. Solve \( 5(2x + 3) = 4x - 7 \).
2. How many solutions does the equation \( 3x - 7 = 5x + 1 \) have?
3. What is the solution to \( 2(3y + 4) = 8 - y \)?
4. Solve for \( z \) in \( -4z + 9 = 3z - 2 \).
5. How many solutions does \( 6x + 4 = 6x + 7 \) have?

**Tip:** When solving equations, always simplify both sides first before moving terms around.

How many solutions does this equation have? 9(–3*j* + 15) = 3 − 15*j*

Learn how to solve the linear equation 9(-3j + 15) = 3 - 15j with a detailed step-by-step solution. This problem involves using the distributive property and basic algebraic manipulation to find that the equation has one solution, j = 11. Suitable for students in Grades 8-10.

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