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3 years ago

5

3x+7= x-1 does x = -4?

1 answer:

vaieri [72.5K]3 years ago

8 0

Subtract x from both sides:
(3x - x) + 7 = (x - x) - 1

3x - x = 2x:
2x + 7 = (x - x) - 1

x - x = 0:
2x + 7 = -1

Subtract 7 from both sides:
2x + (7 - 7) = -7 - 1

7 - 7 = 0:
2x = -7 - 1

-7 - 1 = -8:
2x = -8

Divide both sides by 2:
2x / 2 = -8 / 2

2 / 2 = 1:
x = -8 / 2

The gcd (greatest common denominator) of 8 and 2 is 2:
-8 / 2 = 2(-4) / 2x1 = 2/2 x - 4 = -4

x = -4

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Answer:

a. Not Divisible

b. Divisible

c. Divisible

d. Divisible

e. Divisible

Step-by-step explanation:

To find the divisibility we need to follow the PEMDAS rule and check if the total value can be divided by the selected numbers without returning a remainder.

Let's begin with a:

$16^{5}+215$ by 33

$1,048,576 + 215$

$1,048,791$

We now then divide the total amount with 33.

$\dfrac{1,048,576}{33}$

= 31,781.5454

We can see that the value has a decimal point indicating that the total value divided by 33 will return a remainder. So it is NOT Divisible by 33.

Now let's continue on with the others.

$51^{7}-51^{6}$ by 25

$897,410,677,851 - 17,596,287,801$

$879,814,390,050$

We now then divide the total amount with 25.

$\dfrac{879,814,390,050}{25}$

= 35,192,575,602

The total value did NOT return a decimal point, therefore making the equation true. $51^{7}-51^{6}$ IS divisible by 25.

Next on we have:

$5^{5}-5^{4} +5^{3}$ by 7

$3,125 - 625 + 125$

As we know in the PEMDAS rule, that addition comes first. In this situation we have to read the equation from left to right and solve which ever comes first.

$2,500 + 125$

$2,625$

We now then divide the total amount with 7.

$\dfrac{2,625}{7}$

= 375

The total value did NOT return a decimal point, therefore making the equation true. $5^{5}-5^{4} +5^{3}$ IS divisible by 7.

$7^6+7^5-7^4$ by 11

$117,649+16,807-2,401$

$134,456-2,401$

$132,055$

We now then divide the total amount with 11.

$\dfrac{132,055}{11}$

= 12,005

The total value did NOT return a decimal point, therefore making the equation true. $7^6+7^5-7^4$ IS divisible by 11.

Last but not the least:

$5^{23}-5^{21}$ by 24

$11,920,928,955,078,125-476,837,158,203,125$

$11,444,091,796,875,000$

We now then divide the total amount with 24.

$\dfrac{11,444,091,796,875,000}{24}$

= 476,837,158,203,125

The total value did NOT return a decimal point, therefore making the equation true. $5^{23}-5^{21}$ IS divisible by 24.

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Answer:

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Step-by-step explanation:

Given

Table A to D

Required

Which shows a proportional relationship

To do this, we make use of:

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Where k is the constant of proportionality.

In table (A)

x = 2, y = 4

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$k = \frac{4}{2}$

$k = 2$

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$k = \frac{9}{4}$

$k = 2.25$

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In table (B)

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$k = \frac{y}{x}$

$k = \frac{4}{3}$

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$k = \frac{y}{x}$

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Both values of k are different. Hence, no proportional relationship

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$k = \frac{15}{5}$

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