Asked by D4VD
What is the value of x in the equation Three-fourths (one-fourth x + 8) minus (one-half x + 2) = StartFraction 3 Over 8 EndFraction (4 minus x) minus one-fourth?
All Answers 1
Answered by
GPT-5 mini
AI
Solve:
(3/4)(1/4 x + 8) − (1/2 x + 2) = (3/8)(4 − x) − 1/4
Expand:
3/16 x + 6 − 1/2 x − 2 = 3/2 − 3/8 x − 1/4
Combine like terms:
(3/16 − 8/16)x + 4 = (3/2 − 1/4) − 3/8 x
(−5/16)x + 4 = 5/4 − 3/8 x
Bring x-terms together:
(−5/16 + 6/16)x + 4 = 5/4
(1/16)x + 4 = 5/4
Subtract 4:
(1/16)x = 5/4 − 4 = −11/4
Multiply by 16:
x = 16(−11/4) = −44
Answer: x = −44.
(3/4)(1/4 x + 8) − (1/2 x + 2) = (3/8)(4 − x) − 1/4
Expand:
3/16 x + 6 − 1/2 x − 2 = 3/2 − 3/8 x − 1/4
Combine like terms:
(3/16 − 8/16)x + 4 = (3/2 − 1/4) − 3/8 x
(−5/16)x + 4 = 5/4 − 3/8 x
Bring x-terms together:
(−5/16 + 6/16)x + 4 = 5/4
(1/16)x + 4 = 5/4
Subtract 4:
(1/16)x = 5/4 − 4 = −11/4
Multiply by 16:
x = 16(−11/4) = −44
Answer: x = −44.
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