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3 years ago

Find the value of x in the equation 3(2x-4)-5(x-2)=1

Mathematics

1 answer:

Lyrx [107]3 years ago

4 0

Answer:

x=3

Step-by-step explanation:

3(2x−4)−5(x−2)=1

Step 1: Simplify both sides of the equation.

3(2x−4)−5(x−2)=1

(3)(2x)+(3)(−4)+(−5)(x)+(−5)(−2)=1(Distribute)

6x+−12+−5x+10=1

(6x+−5x)+(−12+10)=1(Combine Like Terms)

x+−2=1

x−2=1

Step 2: Add 2 to both sides.

x−2+2=1+2

x=3

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Simplify each exponential expression using the properties of exponents and match it to the correct answer.

saveliy_v [14]

1) (2 $\times$ 3^-2)^3 (5 $\times$ 3^2)^2 / (3^-2)(5 $\times$ 2)^2 = 2

2) (3^3) (4^0)^2 (3 $\times$ 2)^-3 (2^2) = 1/2

3) (3^7 $\times$ 4^7) (2 $\times$ 5)^-3 (5)^2 / (12^7) (5^-1) (2^-4) = 2

4) (2.3)^-1 (2^0) / (2.3)^-1 = 1

<u>Step-by-step explanation</u>:

Step 1 :

(2 $\times$ 3^-2)^3 (5 $\times$ 3^2)^2 / (3^-2)(5 $\times$ 2)^2

⇒ (2^3) (3^-6) (5^2) (3^4) / (3^-2) (10^2)

⇒ (2.2^2.5^2) (3^-6.3^4) / (3^-2) (10^2)

⇒ (2)(10^2) (3^-2) / (3^-2) (10^2)

⇒ 2

Step 2 :

(3^3) (4^0)^2 (3 $\times$ 2)^-3 (2^2)

Any number with power 'zero' is 1.

⇒ (3^3) (1^2) (3^-3) (2^-3) (2^2)

⇒ (2^(-3+2))

⇒ 2^-1 = 1/2

Step 3 :

(3^7 $\times$ 4^7) (2 $\times$ 5)^-3 (5)^2 / (12^7) (5^-1) (2^-4)

⇒ (12^7) (2^-3) (5^-3) (5^2) / (12^7) (5^-1) (2^-4)

⇒ (2^-3) (5^(-3+2)) / (5^-1) (2^-4)

⇒ (2^-3) (5^-1) / (5^-1) (2^-4)

⇒ 1 / (2^-1)

⇒ 2

Step 4 :

(2.3)^-1 (2^0) / (2.3)^-1

⇒ (2^0)

⇒ Any number with power 'zero' is 1

⇒ 1

8 0

3 years ago

A department store is having a sale of 20% off of all kitchen appliances what is the sale price for a $250 microwave?

ikadub [295]

Answer:

300 dollars

Step-by-step explanation:

250 x 0.2= 50

250 + 50=300

7 0

3 years ago

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If a van traveled 175 miles in 5 hours, how far could the van travel in 8 hours?

Fittoniya [83]

280 because if you divide 175 by 5 you get 35 which is the amount of miles the van travels in 1 hour and then you multiple 35 by 8 and you have your answer 280

5 0

3 years ago

at a particular school with 200 male students, 58 play football, 40 play basketball, and 8 play both. what is the probability th

nignag [31]

this helps (no play) = 121/200 = 0.6050

ifti doesn't I tried

7 0

3 years ago

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What is the answer to > solve 4cos (theta/3) -2 = 0, over [0, 4pi)

Vesna [10]

Hello from MrBillDoesMath!

Answer:

@ = pi/3 (or 60 degrees) or @ = 7 pi/3 (or 420 degrees)

Discussion:

Let "@' denote the angle "theta". We are asked to find @ in the interval [0, 4 pi)

where

4cos(@) - 2 = 0. Adding 2 to both sides

4 cos(@) - 2 +2 = 2 =>

4 cos(@) = 2 Divide both sides by 4

cos(@) = 2/4 = 0.5

This implies that @ = pi/3 (or 60 degrees) or @ = (pi/3 + 2pi) = 7 pi/3 (or 420 degrees)

Thank you,

MrB

5 0

3 years ago