Question
4x+22=8x+10 3x+18=5x+8 what do u notice about these equations
Answers
GPT-4o mini
Let's solve both equations to see what we notice.
### For the first equation:
\[
4x + 22 = 8x + 10
\]
1. Subtract \(4x\) from both sides:
\[
22 = 4x + 10
\]
2. Subtract 10 from both sides:
\[
12 = 4x
\]
3. Divide both sides by 4:
\[
x = 3
\]
### For the second equation:
\[
3x + 18 = 5x + 8
\]
1. Subtract \(3x\) from both sides:
\[
18 = 2x + 8
\]
2. Subtract 8 from both sides:
\[
10 = 2x
\]
3. Divide both sides by 2:
\[
x = 5
\]
### Observations:
1. **Different Solutions:** The two equations have different solutions: \(x = 3\) for the first equation and \(x = 5\) for the second equation. This indicates that the lines represented by these equations intersect the x-axis at different points.
2. **Linear Equations:** Both equations are linear, meaning their graphs would be straight lines.
3. **Variable Coefficients:** The coefficients of \(x\) and the constants in each equation differ, affecting the slope and y-intercept of the lines.
Overall, while both equations are of the same linear form (involving \(x\) terms and constants), they lead to different solutions and have different properties based on their coefficients.
### For the first equation:
\[
4x + 22 = 8x + 10
\]
1. Subtract \(4x\) from both sides:
\[
22 = 4x + 10
\]
2. Subtract 10 from both sides:
\[
12 = 4x
\]
3. Divide both sides by 4:
\[
x = 3
\]
### For the second equation:
\[
3x + 18 = 5x + 8
\]
1. Subtract \(3x\) from both sides:
\[
18 = 2x + 8
\]
2. Subtract 8 from both sides:
\[
10 = 2x
\]
3. Divide both sides by 2:
\[
x = 5
\]
### Observations:
1. **Different Solutions:** The two equations have different solutions: \(x = 3\) for the first equation and \(x = 5\) for the second equation. This indicates that the lines represented by these equations intersect the x-axis at different points.
2. **Linear Equations:** Both equations are linear, meaning their graphs would be straight lines.
3. **Variable Coefficients:** The coefficients of \(x\) and the constants in each equation differ, affecting the slope and y-intercept of the lines.
Overall, while both equations are of the same linear form (involving \(x\) terms and constants), they lead to different solutions and have different properties based on their coefficients.