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zimovet [89]
3 years ago
12

(02.03 MC)

Mathematics
1 answer:
vodomira [7]3 years ago
4 0

Answer:

So the Solution is

x = 4\ , x = -2

Step-by-step explanation:

Solve for x: 4|2x − 2| + 10 = 34.

Step 1. Subtracting 10 on both the sides we get

4|2x-2|+10-10=34-10\\\\4|2x-2|=24

Step 2. Dividing both the side by 4 we get

\dfrac{4|2x-2|}{4}=\dfrac{24}{4}\\\\|2x-2|=6

Step 3. Removing Modulus sign we get two values

2x-2=6\ or\ 2x-2=-6\\\\2x=6+2\ or\ 2x=-6+2\\\\2x=8\ or\ 2x=-4\\\\x=\dfrac{8}{2} \ or\ x=\dfrac{-4}{2} \\\\x=4\ or\ x=-2\\

So the Solution is

x = 4\ , x = -2

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Prove the sum of three consecutive is divisible by three, that the sum of 5 consecutive integers is divisible by 5, but the sum
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Answer:

Proved

Step-by-step explanation:

Solving (a):

Let the numbers be: x, x + 1, x + 2.

Their sum is:

Sum = x + x + 1 + x + 2

Collect Like Terms

Sum = x + x + x + 1 + 2

Sum = 3x + 3

Divide sum by 3.

Result = \frac{Sum}{3}

Result = \frac{3x+3}{3}

Result = \frac{3(x+1)}{3}

Result = x + 1

<em>Hence, this is true because there is no fractional part after the division</em>

<em></em>

Solving (b):

Let the numbers be: x, x + 1, x + 2,x+3,x+4

Their sum is:

Sum = x + x + 1 + x + 2+x + 3 + x + 4

Collect Like Terms

Sum = x + x + x + x + x+1  + 2 + 3 + 4

Sum = 5x+10

Divide sum by 5.

Result = \frac{5x + 10}{5}

Result = \frac{5(x + 2)}{5}

Result = x + 2

<em>Hence, this is true because there is no fractional part after the division</em>

<em></em>

Solving (c):

Let the numbers be: x, x + 1, x + 2,x+3

Their sum is:

Sum = x + x + 1 + x + 2+x + 3

Collect Like Terms

Sum = x + x + x + x + 1  + 2 + 3

Sum = 4x+6

Divide sum by 4.

Result = \frac{4x + 6}{4}

Split

Result = \frac{4x}{4} + \frac{6}{4}

Result = x + 1.5

<em>The 1.5 means that the sum can not be divisible by 4</em>

5 0
3 years ago
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