Question
Solve using inverse operations. Use the sketch pad to show your work: -4+2b=-40
Answers
GPT-4o mini
To solve the equation \(-4 + 2b = -40\) using inverse operations, we can follow these steps:
1. **Add 4 to both sides** of the equation to isolate the term with \(b\) on one side:
\[
-4 + 2b + 4 = -40 + 4
\]
\[
2b = -36
\]
2. **Divide both sides** by 2 to solve for \(b\):
\[
\frac{2b}{2} = \frac{-36}{2}
\]
\[
b = -18
\]
So, the solution to the equation \(-4 + 2b = -40\) is \(b = -18\).
If you were to use a sketch pad, you could represent each of these steps visually, showing the balance of the equation at each stage. You could diagrammatically show adding 4 to both sides, and then dividing both sides by 2, visualizing how each operation maintains the balance of the equation.
1. **Add 4 to both sides** of the equation to isolate the term with \(b\) on one side:
\[
-4 + 2b + 4 = -40 + 4
\]
\[
2b = -36
\]
2. **Divide both sides** by 2 to solve for \(b\):
\[
\frac{2b}{2} = \frac{-36}{2}
\]
\[
b = -18
\]
So, the solution to the equation \(-4 + 2b = -40\) is \(b = -18\).
If you were to use a sketch pad, you could represent each of these steps visually, showing the balance of the equation at each stage. You could diagrammatically show adding 4 to both sides, and then dividing both sides by 2, visualizing how each operation maintains the balance of the equation.