How many solutions does this equation have?



–18*t* + 19 = –18*t* − 16 − 7t

Let's determine how many solutions the equation has by solving it step-by-step.

The given equation is:
\[
-18t + 19 = -18t - 16 - 7t
\]

### Step 1: Simplify the equation
First, combine like terms on the right side of the equation:
\[
-18t + 19 = -18t - 16 - 7t
\]
\[
-18t + 19 = -18t - 7t - 16
\]
\[
-18t + 19 = -25t - 16
\]

### Step 2: Eliminate the \(-18t\) term
Add \(18t\) to both sides to eliminate the \(-18t\) term:
\[
19 = -7t - 16
\]

### Step 3: Solve for \(t\)
Now, isolate \(t\) by adding 16 to both sides:
\[
19 + 16 = -7t
\]
\[
35 = -7t
\]

Finally, divide both sides by \(-7\):
\[
t = \frac{35}{-7}
\]
\[
t = -5
\]

### Conclusion:
The equation has **one solution**, and that solution is \(t = -5\).

Would you like more details or have any questions?

Here are 5 related questions to expand on this topic:
1. How do you verify the solution of a linear equation?
2. What are the steps to isolate the variable in a linear equation?
3. How do equations with one variable differ from those with two variables?
4. Can a linear equation have no solutions? If so, how can you tell?
5. What are some common mistakes to avoid when solving linear equations?

**Tip:** Always check your solution by substituting it back into the original equation to ensure it satisfies the equation.

Learn how to solve the linear equation -18t + 19 = -18t - 16 - 7t with a step-by-step solution. This problem covers isolating variables in linear equations. Suitable for students in Grades 7-9.

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