4x+22=8x+10 5x+5=5x+4
the original equations and check to show that they can have no
solution. Explain your work.
Let's look at the first equation:
4x + 22 = 8x + 10
Let's try to isolate x by subtracting 4x from both sides of the equation:
4x - 4x + 22 = 8x - 4x + 10
This simplifies to:
22 = 4x + 10
Now, we'll subtract 10 from both sides:
22 - 10 = 4x + 10 - 10
which further simplifies to:
12 = 4x
Now, we'll divide both sides by 4:
12 / 4 = 4x / 4
which gives us:
3 = x
So, x = 3 is the solution for the first equation.
Now, let's look at the second equation:
5x + 5 = 5x + 4
Notice that both sides have the same coefficient for x (5). So, we can try to subtract 5x from both sides to see if there's a solution:
5x - 5x + 5 = 5x - 5x + 4
This simplifies to:
5 = 4
However, 5 cannot be equal to 4. This means that the second equation has no solution.
In summary, the first equation has a solution (x=3), while the second equation has no solution.