Answer
The solution is:
$$z = -1.875$$
To check this solution, we plug $-1.875$ into the original equation:
$$1.4(-1.875 - 5) - 0.2 = 0.5(6(-1.875) - 8))$$
Distribute to simplify:
$$-2.625 - 7 - 0.2 = 0.5(11.25 - 8)$$
$$-2.625 - 7 - 0.2 = 5.625 - 4$$
Simplify both sides of the equation to get:
$$-9.825 = 0.5 (-19.25)$$
$$-9.625 = -9.625$$
Since both sides of the equation are equal to one another, we know that our solution is correct.
Work Step by Step
Use distributive property to simplify:
$$1.4z - (1.4)(5) = (0.5)(6z) - (0.5)(8)$$
Let's move variables to one side and constants to the other side:
$$1.4z - (0.5)(6z) = (1.4)(5) - (0.5)(8)$$
Multiply to simplify:
$$1.4z - 3z = 7 - 4$$
$$-1.6z = 3$$
$$z = -1.875$$
To check this solution, we plug $-1.875$ into the original equation:
$$1.4(-1.875 - 5) - 0.2 = 0.5(6(-1.875) - 8))$$
Distribute to simplify:
$$-2.625 - 7 - 0.2 = 0.5(11.25 - 8)$$
$$-2.625 - 7 - 0.2 = 5.625 - 4$$
Simplify both sides of the equation to get:
$$-9.825 = 0.5 (-19.25)$$
$$-9.625 = -9.625$$
Since both sides of the equation are equal to one another, we know that our solution is correct.
