Advertisements
Advertisements
Question
Solve:
`5x − (4x + (5x - 4)/7) = (4x - 14)/3`
Advertisements
Solution
`5x − (4x + (5x - 4)/7) = (4x - 14)/3`
Distribute the negative sign: `5x-4x-(5x-4)/7`
Simplify: `x- (5x-4)/7`
The LHS becomes: `x- (5x-4)/7`
`x - (5x-4)/7 = (4x-14)/3`
Multiply through by the least common denominator (LCD), which is 21, to eliminate fractions:
`21 (x- (5x-4)/7) = 21. (4x-14)/3`
Distribute 21 on both sides:
21x − 3(5x − 4) =7(4x − 14).
Simplify: 21x − 15x + 12 = 28x − 98.
Combine like terms: 6x + 12 = 28x − 98.
Bring all x-terms to one side and constants to the other: 6x − 28x = −98 − 12.
−22x = −110.
Solve for x: `x = (-110)/-22`
= 5
APPEARS IN
RELATED QUESTIONS
Solve the following equation:
`("x" - 1)/("7x" - 14) = ("x" - 3)/("7x" - 26)`
Solve: `"2x"/3 - ("x" - 1)/6 + ("7x" - 1)/4 = 2 1/6` Hence, find the value of 'a', if `1/"a" + 5"x" = 8`
Fifteen less than 4 times a number is 9. Find the number.
Five less than 3 times a number is -20. Find the number.
A number decreased by 30 is the same as 14 decreased by 3 times the number; Find the number.
The present age of a man is twice that of his son. Eight years hence, their ages will be in the ratio 7 : 4. Find their present ages
Solve: `2/"5x" - 5/"3x" = 1/15`
Solve: `"x" - ("x" - 1)/2 = 1 - ("x" - 2)/3`
The ages of A and B are in the ratio 7 : 5. Ten years hence, the ratio of their ages will be 9 : 7. Find their present ages.
The numerator of a fraction is 5 less than its denominator. If 3 is added to the numerator, and denominator both, the fraction becomes`4/5`. Find the original fraction.
