Question

Solve the following equation. 2/3 x + 6 = 1/2x + 1/4x

A. 6
B. 72
C. 14 2/5
D. 2

Answer 1

QUESTION:

Solve the following equation 2/3 x + 6 = 1/2 x + 1/4x

ANSWER:

In all choices the correct answer is B
`\blue{\boxed{72}}`

STEP-BY-STEP Step-by-step explanation:

`\blue{\boxed{Note:}}` Since x is on the right side of the equation, switch the sides so it is on the left side of the equation

`(1)/(2) x + (1)/(4) x = (2)/(3) x + 6`

First, Simply each term

Combine
`{(1)/(2)}`,
`{(1)/(4)}` to x

`(x)/(2) + (x)/(4) = (2)/(3) x + 6`

`\blue{\boxed{Note:}}` To write
`{(x)/(2)}` as a fraction with a common denominator, multiply by
`{(2)/(2)}`

`(x)/(2) * (2)/(2) + (x)/(4) = (2)/(3) x + 6`

Second, Write each expression with a common denominator of 4, by multiplying each by appropriate factor of 1

Multiply
`{(x)/(2)}` and
`{(2)/(2)}`

`(x * 2)/(2 * 2) + (x)/(4) = (2)/(3) x + 6`

Multiply 2 and 2

`(x * 2)/(4) + (x)/(4) = (2)/(3) x + 6`

`\blue{\boxed{Note:}}` Combine the numerators over the common denominator

`(x * 2 + x)/(4) = (2)/(3) x + 6`

Third, Simplify the numerator

Move 2 to the left of x

`(2 * x + x)/(4) = (2)/(3) x + 6`

Add 2x and x

`(3x)/(4) = (2)/(3) x + 6`

`\blue{\boxed{Note:}}` Combine
`{(2)/(3)}` and x

`(3x)/(4) = (2x)/(3) + 6`

Fourth, Move all terms containing x to the left side of the equation

Subtract
`{(2x)/(3)}` from both sides of the equation

`(3x)/(4) - (2x)/(3) = 6`

`\blue{\boxed{Note:}}` To write
`{(3x)/(4)}` as a fraction with a common denominator, multiply by
`{(3)/(3)}`

`(3x)/(4) * (3)/(3) - (2x)/(3) = 6`

`\blue{\boxed{Note Again:}}` To write
`{(-2x)/(3)}` as a fraction with a common denominator, multiply by
`{(4)/(4)}`

`(3x)/(4) * (3)/(3) - (2x)/(3) * (4)/(4) = 6`

Fifth, Write each expression with a common denominator of 12, by multiplying each by an appropriate factor of 1

Multiply
`{(3x)/(4)}` and
`{(3)/(3)}`

`(3x * 3)/(4 * 3) - (2x)/(3) * (4)/(4) = 6`

Multiply 4 and 3

`(3x * 3)/(12) - (2x)/(3) * (4)/(4) = 6`

Multiply
`{(2x)/(3)}` and
`{(4)/(4)}`

`(3x * 3)/(12) - (2x * 4)/(3 * 4) = 6`

Multiply 3 and 4

`(3x * 3)/(12) - (2x * 4)/(12) = 6`

`\blue{\boxed{Note:}}` Combine the numerators over the common denominator

`(3x * 3 - 2x * 4)/(12) = 6`

Sixth, Simplify the numerator

Factor x out of 3x ×3 - 2x × 4

`(x(3 * 3 - 2 * 4))/(12) = 6`

Multiply 3 by 3

`(x(9 - 2 * 4))/(12) = 6`

Multiply - 2 by 4

`(x(9 - 8))/(12) = 6`

Subtract 8 from 9

`(x * 1)/(12) = 6`

Multiply x by 1

`(x)/(12) = 6`

`\blue{\boxed{Note:}}` Multiply both sides of the equation by 12

`12 * (x)/(12) = 12 * 6`

Seventh, Simplify both sides of the equation and cancel the common factor of 12

Cancel the common factor

`12 * (x)/(12) = 12 * 6`

Rewrite the expression

`x = 12 * 6`

Lastly, Multiply 12 by 6

`\blue{\boxed{ x = 72}}`

hope it's helps