compare and contrast: below are two equations. solve each equation and compare the two solutions. choose the statement that is true about each solution. equation #1 2x-3=-17 5x+3=12
A. equation #1 and equation #2 have the same number of solutions
B. equation #1 has more solutions than equation #2
C. equation #1 has fewer solutions than equation #2
I think C
since each equation is a straight line, each has exactly one solution.
Think on it. A solution is where the graph intersects the x-axis. Two distinct lines intersect in exactly one point, unless they are parallel.
To solve equation #1, we can first isolate the variable by adding 3 to both sides:
2x - 3 + 3 = -17 + 3
2x = -14
Next, we can solve for x by dividing both sides by 2:
2x/2 = -14/2
x = -7
So, the solution to equation #1 is x = -7.
Now, let's solve equation #2:
5x + 3 = 12
We can isolate the variable x by subtracting 3 from both sides:
5x + 3 - 3 = 12 - 3
5x = 9
Next, by dividing both sides by 5, we can solve for x:
5x/5 = 9/5
x = 9/5 or x = 1.8
So, the solution to equation #2 is x = 1.8.
Comparing the two solutions, we have x = -7 for equation #1 and x = 1.8 for equation #2. As the two solutions are different, the statement that is true about each solution is:
B. Equation #1 has more solutions than Equation #2.