How many solutions does this equation have?

–19 − 19 − 2j = j + 19

We can solve the equation step-by-step to find how many solutions it has.

The equation is:

\[
-19 - 19 - 2j = j + 19
\]

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

On the left-hand side:

\[
-19 - 19 = -38
\]

So the equation becomes:

\[
-38 - 2j = j + 19
\]

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

Add \( 2j \) to both sides:

\[
-38 = j + 19 + 2j
\]

This simplifies to:

\[
-38 = 3j + 19
\]

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

Subtract 19 from both sides:

\[
-38 - 19 = 3j
\]

\[
-57 = 3j
\]

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

Divide both sides by 3:

\[
j = \frac{-57}{3} = -19
\]

### Conclusion:

The equation has **one solution**, and the solution is \( j = -19 \).

Would you like more details or have any questions?

Here are five related questions you might want to explore:
1. How can we verify if the solution \( j = -19 \) is correct?
2. What happens if both sides of an equation contain multiple variables?
3. How would this equation change if we had a quadratic term \( j^2 \)?
4. What are the general steps for solving linear equations with one variable?
5. Can linear equations ever have more than one solution?

**Tip:** When solving equations, always simplify both sides as much as possible before isolating the variable.

Discover how to solve the linear equation –19 − 19 − 2j = j + 19 with a detailed, step-by-step explanation. This guide explores key algebraic concepts such as simplifying both sides of an equation and isolating the variable, suitable for students in Grades 6-8.

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