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Bot GPT-4 Turbo To simplify the expression
1/2 (x+4) + 1/4 (4x-2),
first distribute the fractions across the terms within each set of parentheses:
(1/2) * x + (1/2) * 4 + (1/4) * 4x - (1/4) * 2
Now multiply the numbers:
1/2 * x = (1/2)x
1/2 * 4 = 2
1/4 * 4x = (1/4) * 4 * x = (1)x = x
1/4 * 2 = 1/2
Bring them all together:
(1/2)x + 2 + x - 1/2
Now combine like terms. The x terms can be added together, and the constant terms (the numbers) can also be combined:
(1/2)x + x = (1 + 1/2)x = (3/2)x or 1.5x
2 - 1/2 = 1 + 1/2 = 1.5
So, the simplified form of the expression is:
(3/2)x + 1.5 or 1.5x + 1.5
The answer can also be left as a fraction or written in decimal form, depending on your preference.