Final answer:
To solve the equation 0.5z + 1.4 = 0.4z - 0.1, subtract 0.4z from both sides to obtain 0.1z + 1.4 = -0.1. Then subtract 1.4 from both sides to get 0.1z = -1.5, and finally, divide by 0.1 to find z = -15.
Step-by-step explanation:
To solve the equation 0.5z + 1.4 = 0.4z - 0.1, we first want to isolate the variable z by getting all the z terms on one side and the constants on the other. We can do this by subtracting 0.4z from both sides, which gives us:
0.5z - 0.4z + 1.4 = -0.1
This simplifies to:
0.1z + 1.4 = -0.1
Next, we subtract 1.4 from both sides to solve for z:
0.1z = -1.5
Finally, we divide both sides by 0.1, which gives us:
z = -15
This is the solution to the given equation.