Twice the difference of a number and 2 is equal to three times the sum of a number and 2. Find the number

x = -10

Step-by-step explanation:

to solve this world problem we say let the number be x

now,

let the difference of a number and 2 = (x -2)

twice the difference of a number will be interpreted as

2( x -2)

also,

let the sum of a number be = (x + 2)

three times the sum of a number = 3(x+2)

2(x-2) = 3( x+ 2)

2x - 4 = 3x + 6

collect the like terms

2x - 3x = 6 + 4

-x = 10

divide both sides by -

-x/- = 10/-

x = -10

therefore the number is equal to 10

to check if your answer is correct put the value of x = -10 into the expression and evaluate to check if the right hand side is equal to the left hand side.

2( -10 -2) = 3( -10 +2)

-20 -4 = -30+ 6

-24 =  -24 proved

(a) the volume of the cone is 20/3 in3

hence, option a is correct.

rick has $1400 and sally has $1500

step-by-step explanation:

to find amount of money rick has after 10 years :

principal = $1000 , time = 10 years , rate = 4% annually

to find amount of money sally has after 10 years :

her friend gives to pay her $50 per year, therefore money she has after 10 years = 50 × 10 = $500

also, sally gets $1000 after 10 years,

therefore, total amount of money sally has after 10 years = 500 + 1000 = $1500

so, after 10 years : rick has $1400 and sally has $1500