Is the following sentence grammatically correct? Why or why not? "The boy loved to eat dinner with his family, after he finished he would start his homework."
The sentence has TWO grammar errors. The first error is a comma splice - there should be a ";" (semi-colon) between "family" and "after" because they are two independent clauses. Secondly, there should be a comma after "finished", because it signifies the end of the prepositional phrase.
If x = 4 and y = 2, how much larger is the value of 3x^2 – 6y than the value of 6x – y^2 ?
The answer is 20! If we plug in the given values, we can see that the first expression yields 3(4^2)-6(2) and the second expression gives us 6(4)-(2^2). After simplifying, we can see that the first expression is 36 (3*16 = 48, 48-12 = 36). The second expression gives us 20 (24-4=20). But that's not all! We must figure out how much larger the first is than the second, so we must subtract 36 - 20 to get our answer, which is 16.
Solve for x: 5(-4x - 2) - (x + 3) = -4(4x + 5) + 12
The answer is x = -1! We know this because if multiply to coefficients for the appropriate terms on either side, we get -20x-10-x-3=-16x-20+12. After simplifying and combining like terms, we get the equation -21x-13=-16x-8. Combining like terms on either side of the equation, we get -5x=5, and we can simplify that to get x=-1!