Question

6 1/4 (x− 2/3 )=9 3/8

Answer 1

`\huge\boxed{x=(13)/(6)=2(1)/(6)}`

Explanation:

`\text{Convert mixed numbers to the improper fractions}\\\\6(1)/(4)=((6)(4)+1)/(4)=(25)/(4)\\\\9(3)/(8)=((9)(8)+3)/(8)=(75)/(8)\\\\6(1)/(4)\left(x-(2)/(3)\right)=9(3)/(8)\to(25)/(4)\left(x-(2)/(3)\right)=(75)/(8)\qquad\text{use the distributive property}\\\\\left((25)/(4)\right)(x)-\left((25)/(4)\right)\left((2)/(3)\right)=(75)/(8)\\\\(25)/(4)x-(50)/(12)=(75)/(8)`

`(25)/(4)x-(25)/(6)=(75)/(8)\qquad\text{multiply both sides by LCD = 24}\\\\24\cdot(25)/(4)x-24\cdot(25)/(6)=24\cdot(75)/(8)\\\\(6)(25)x-(4)(25)=(3)(75)\\\\150x-100=225\qquad\text{add 100 from both sides}\\\\150x=325\qquad\text{divide both sides by 150}\\\\x=(325)/(150)\\\\x=(325:25)/(150:25)\\\\x=(13)/(6)`

Answer 2

2⅙

Explanation:

6¼(x - ⅔) = 9⅜

(25/4)(x - ⅔) = 75/8

x - ⅔ = 75/8 × 4/25

x - ⅔ = 1½

x = 1½ + ⅔

Lcm is 6

x = 1 + (3+4)/6

x = 1 + 7/6

x = 2⅙