Question

1/3 x equals 6 - 1/5 x

Answer 1

`(1)/(3)x=6-(1)/(5)x\qquad\text{multiply both sides by 15}\\\\15\cdot(1)/(3)x=15\cdot6-15\cdot(1)/(5)x\\\\5x=90-3x\qquad\text{add 3x to both sides}\\\\8x=90\qquad\text{divide both sides by 8}\\\\x=(90)/(8)\\\\x=(45)/(4)\\\\x=11(1)/(4)\to x=11.25`

Answer 2

(1/3)x = 6 - (1/5)x Add (1/5) x to both sides.

(1/3)x + (1/5)x = 6 Find the Lowest common denominator of 1/3 and 1/5. Both are primes.

3 has 3 as a part of the LCD.

5 has 5 as part of the LCD

LCD: 3 * 5 The LCM is the number of needed primes (3 and 5 in this case) multiplied together.

LCD: 15

1/3 = 1 * 5 / (3 * 5) = 5/15 Equivalent to 1/3

1/5 = 1 * 3 / (3 * 5) = 3/15 Equivalent to 1/5

(5/15)x + (3/15)x = 6 Add the fractions

(8/15)x = 6 Change 8/15 to a decimal

0.53333333 x = 6 Divide by 0.5333333 on both sides.

x = 6/ 0.533333333 Make sure you use as much of the repeating decimal as you can. This method saves you having to divide by a fraction.

x = 11.25