Introductory Algebra for College Students (7th Edition)

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.
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.