Introductory Algebra for College Students (7th Edition)

$$x = 7700$$ To check if we have the correct solution, let us plug $7700$ into the original equation for $x$. If both sides of the equation equal one another, then the solution is correct: $$0.6(7700 + 300) = 0.65(7700) - 205$$ Let's evaluate what is inside the parentheses first: $$0.6(8000) = 0.65(7700) - 205$$ Multiply first: $$4800 = 5005 - 205$$ Lastly, we do the subtraction: $$4800 = 4800$$ Both sides of the equation are equal, so we know our solution is correct.
To solve this equation, we work step-by-step to isolate the variable on one side and the constant on the other. To do this, we use the order of operations, represented by the acronym PEMDAS. This means that we evaluate parentheses first, then exponents and radicals, then multiplication and division, and, finally, addition and subtraction. In this problem, we use distributive property first to get rid of all the parentheses: $$0.6(x) + 0.6(300) = 0.65x - 205$$ We now multiply out the terms: $$0.6x + 180 = 0.65x - 205$$ Subtract $0.6x$ from both sides of the equation to isolate the variable to one side of the equation: $$180 = 0.05x - 205$$ Add $205$ to both sides of the equation to isolate the constants to the other side of the equation: $$385 = 0.05x$$ Divide both sides of the equation by $0.05$ to solve for $x$: $$x = 7700$$ To check if we have the correct solution, let us plug $7700$ into the original equation for $x$. If both sides of the equation equal one another, then the solution is correct: $$0.6(7700 + 300) = 0.65(7700) - 205$$ Let's evaluate what is inside the parentheses first: $$0.6(8000) = 0.65(7700) - 205$$ Multiply first: $$4800 = 5005 - 205$$ Lastly, we do the subtraction: $$4800 = 4800$$ Both sides of the equation are equal, so we know our solution is correct.