30 POINTS! Please answer and show work for both!

1 answer:

monitta3 years ago

6 0

The recommended approach for such equations is to eliminate fractions first, by multiplying by the LCM of the denominators. You can simply simplify, then work them as a 2-step linear equation, doing your arithmetic with the fractions as they are.

a) (5x-1)/7 + (4x-3)/2 -(3-2x)/2 = 6 . . . . . given

... 2(5x -1) +7(4x -3) -7(3 -2x) = 84 . . . . . multiply by 14

... 10x -2 +28x -21 -21 +14x = 84 . . . . . . eliminate parentheses

... 52x -44 = 84 . . . . . . . . . . . . . . . . . . . . collect terms

... 52x = 128 . . . . . . . . . . . . . . . . . . . . . . . add 44

... x = 32/13 . . . . . . . . . . . . . . . . . . . . . . . . divide by 52 and simplify

b) (4x−3)/2 − (5−2x)/3 − (3x−4)/3 = 5 . . . given

... 2x -3/2 -5/3 +(2/3)x -x +4/3 = 5 . . . . . . .eliminate parentheses

... (5/3)x -11/6 = 5 . . . . . . . . . . . . . . . . . . . . simplify

... (5/3)x = 41/6 . . . . . . . . . . . . . . . . . . . . . . add 11/6

... x = (41/6)/(5/3) = 41/10 . . . . . . . . . . . . . .divide by the coefficient of x

_____

Using the first method, you're dealing with integers and you can do a lot of the math in your head. Using the second method, you're dealing with fractions and mixed numbers. A calculator can be helpful, especially if it handles arithmetic with fractions nicely, as many graphing calculators do.

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Sergeeva-Olga [200]

Answer:

Step-by-step explanation:

just multiply 2 on both sides

7 0

3 years ago

Show 2 different solutions to the task.

laila [671]

Answer with Step-by-step explanation:

1. We are given that an expression $n^2+n$

We have to prove that this expression is always is even for every integer.

There are two cases

1.n is odd integer

2.n is even integer

1.n is an odd positive integer

n square is also odd integer and n is odd .The sum of two odd integers is always even.

When is negative odd integer then n square is positive odd integer and n is negative odd integer.We know that difference of two odd integers is always even integer.Therefore, given expression is always even .

2.When n is even positive integer

Then n square is always positive even integer and n is positive integer .The sum of two even integers is always even.Hence, given expression is always even when n is even positive integer.

When n is negative even integer

n square is always positive even integer and n is even negative integer .The difference of two even integers is always even integer.

Hence, the given expression is always even for every integer.

2.By mathematical induction

Suppose n=1 then n= substituting in the given expression

1+1=2 =Even integer

Hence, it is true for n=1

Suppose it is true for n=k

then $k^2+k$ is even integer