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Juliette [100K]
3 years ago
14

What value of x makes the equation 3(x-6)-8x=-2+5(2x+1) true ?

Mathematics
1 answer:
Dafna11 [192]3 years ago
5 0

Answer:

x = (-7)/5

Step-by-step explanation:

Solve for x:

3 (x - 6) - 8 x = 5 (2 x + 1) - 2

3 (x - 6) = 3 x - 18:

3 x - 18 - 8 x = 5 (2 x + 1) - 2

Grouping like terms, 3 x - 8 x - 18 = (3 x - 8 x) - 18:

(3 x - 8 x) - 18 = 5 (2 x + 1) - 2

3 x - 8 x = -5 x:

-5 x - 18 = 5 (2 x + 1) - 2

5 (2 x + 1) = 10 x + 5:

-5 x - 18 = 10 x + 5 - 2

Add like terms. 5 - 2 = 3:

-5 x - 18 = 10 x + 3

Subtract 10 x from both sides:

(-5 x - 10 x) - 18 = (10 x - 10 x) + 3

-5 x - 10 x = -15 x:

-15 x - 18 = (10 x - 10 x) + 3

10 x - 10 x = 0:

-15 x - 18 = 3

Add 18 to both sides:

(18 - 18) - 15 x = 18 + 3

18 - 18 = 0:

-15 x = 3 + 18

3 + 18 = 21:

-15 x = 21

Divide both sides of -15 x = 21 by -15:

(-15 x)/(-15) = 21/(-15)

(-15)/(-15) = 1:

x = 21/(-15)

The gcd of 21 and -15 is 3, so 21/(-15) = (3×7)/(3 (-5)) = 3/3×7/(-5) = 7/(-5):

x = 7/(-5)

Multiply numerator and denominator of 7/(-5) by -1:

Answer: x = (-7)/5

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Ab=45 mm,bc=10cm 4mm ,cd = 5 cm 6 mm ,de= 35 mm,ea=x cm, and the perimeter of irregular pentagon is 280 mm. Find the length of t
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Answer:

The length of the unknown side x is 4 cm

Step-by-step explanation:

we know that

The perimeter of a polygon is equal to the sum of its length sides

Remember that

1 cm=10 mm

In this problem we have

AB=45 mm ------> convert to cm -----> AB=45/10=4.5 cm

BC=10 cm 4 mm -----> convert to cm -----> BC=10+4/10=10.4 cm

CD=5 cm 6 mm  -----> convert to cm -----> CD=5+6/10=5.6 cm

DE=35 mm ------> convert to cm -----> DE=35/10=3.5 cm

EA=x cm

P=280 mm ------> convert to cm -----> P=280/10=28 cm

The perimeter of the irregular polygon is equal to

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substitute the values

28=4.5+10.4+5.6+3.5+x

28=24+x

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3 0
3 years ago
jeds market has a total of 26 employees. Each full time employee makes $275/ week, and each part-time employee makes $140/ week.
ollegr [7]

The number of full time employees is 17 and the number of part time employee is 9

Step-by-step explanation:

Step 1 :

Let f represent the number of full time employee and p represent the number of part time employee

Total number of employees = 26

Hence we have f + p = 26

Step 2 :

Wages of full time employee  = $275

Wages of part time employee = $140

Total wages paid by Jeds = $ 5935

Hence we have 275 f + 140 p = 5935

Step 3:

Solving the equations obtained in step 1 and step 2 we have

f + p = 26, Multiplying by 275 = > 275 f + 275 p = 7150

275 f + 140 p = 5935

Subtracting equation 2 from 1 we have

135 p = 1215 => p = 9

Substituting this in f + p = 26 gives, f + 9 = 26

So f = 17

Step 4 :

Answer :

The number of full time employees is 17 and the number of part time employee is 9

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X ÷ 4 = 8

Multiply each side by 4

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He subtracted 4 from 12 and got 8

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