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Question
Solve:
`5x − (4x + (5x - 4)/7) = (4x - 14)/3`
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
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