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VashaNatasha [74]
3 years ago
12

Two students solved the same multi-step equation. Which student is correct? Explain the error. Student A Student B 2x - 4(3x + 6

) = -6(2x + 1) - 4 2x - 4(3x + 6) = -6(2x + 1) - 4 2x - 12x + 6 = -12x + 1 - 4 2x - 12x - 24 = -12x - 6 - 4 -10x + 6 = -12x - 3 -10x - 24 = -12x - 10 2x = -9 2x = 14 x = -4 _1 2 x = 7
Mathematics
1 answer:
Gnom [1K]3 years ago
8 0

Answer:

Student B is correct

Student A failed to distribute -4 and -6 when opening the brackets in the first step

Step-by-step explanation:

The solution Student A gave was:

2x - 4(3x + 6) = -6(2x + 1) - 4

2x - 12x + 6 = -12x + 1 - 4

-10x + 6 = -12x - 3

2x = -9

x = -4 _1 2 ( -4 1/2)

The solution Student B gave was:

2x - 4(3x + 6) = -6(2x + 1) - 4

2x - 12x - 24 = -12x - 6 - 4

-10x - 24 = -12x - 10

2x = 14

x = 7

Student B is correct.

Explanation of the error:

Student A failed to distribute -4 and -6 when opening the brackets in the first step.

That is,

2x - 4(3x + 6) = -6(2x + 1) - 4

To open this bracket, we will distribute, -4 and -6 so that we get

2x (-4 × 3x) + (-4 × +6) = (-6×2x) + (-6 × +1) - 4

Then we will get

2x -12x -24 = -12x -6 -4

Adding the like terms

-10x - 24 = -12x - 10

Collecting like terms

-10x + 12x = -10 + 24

∴ 2x = 14

x = 14 / 2

Hence,

x = 7

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Answer:

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Step-by-step explanation:

So we are subtracting a negative which is the same as adding.  Our equation becomes -1/3+1/2.  To add fractions we need a common denominator (the denominator of a fraction is the number on the bottom)  To fine the least common denominator we need to find the lowest number that both 3 and 2 go into which is 6.  Then we will multiply each fraction by the number that will give us 6 for a denominator which is 2 for -1/3 and 3 for 1/2.  So -1/3 times 2 is -2/6 and 1/2 times 3 is 3/6.  Our equation is now -2/6+3/6.  Now we will add the numerators ( the numerator is the number on the top of the fraction) and the denominators stay the same when adding or subtraction fractions -2/6+3/6=1/6

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Answer:

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Step-by-step explanation:

Given  f ( x ) =2 x ^2 − 18/x^2-16

find all asymptotes, holes and intercepts.

Factor the numerator and denominator.

f ( x ) =2 ( x ^2 − 9 )/( x + 4 ) ( x − 4 )

f ( x ) =2 ( x +3 ) ( x − 3 )/( x + 4 ) ( x − 4 )

A hole exists when the numerator and denominator contain the same factor (a factor "cancels out"). This function has no holes.

To find the vertical asymptote(s) (VA), find the values of  x

which make the denominator equal zero. The function is undefined at these values of  x

because you cannot divide by zero.

Set each factor of the denominator equal to zero and solve.

x + 4 = 0  and x − 4 = 0

x = − 4  and  x = 4

These are the VAs.

To find the horizontal asymptote(HA), compare the degree of the numerator and denominator. If the degrees are the same, the HA is the ratio of the leading coefficients.

For  f ( x) =2 x ^2 − 18/x^2-16

the degree in both numerator and denominator is  2

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The HA is  x = 2

The  x  intercept is the value at which the function (or "y") equals zero. If the numerator is zero, the function equals zero.

2 ( x + 3 ) ( x − 3 ) = 0

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The  x  intercepts are  ( − 3 , 0 )  and  ( 3 , 0 ) .

The  y  intercepts are found by setting  x = 0 .

f ( 0 ) = 2 ( 0 ) ^2 − 18/( 0 )^2 − 16 = 9 /8

The  y  intercept is  ( 0 , 9/ 8 ) .

graph{(2x^2-18)/(x^2-16) [-10.04, 9.96, -3.56, 6.44]}

HOPE THIS HELPS YOU!!!!

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Step-by-step explanation:

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