Answer:
x = 381/24 = 3 29/84
Step-by-step explanation:
7x + 1/2(x + 1/4) = 3(6x - 9) - 8
<em>Use the distributive property to multiply 1/2 by x + 1/4.</em>
7x + 1/2x + 1/8 = 3(6x - 9) - 8
<em>Combine 7x (14/2x) and 1/2x to get 15/2</em>.
15/2x + 1/8 = 3(6x - 9) - 8
<em>Use the distributive property to multiply 3 by 6x - 9.</em>
15/2x + 1/8 = 18x - 27 - 8
<em>Subtract 8 from -27 to get -35.</em>
15/2x + 1/8 = 18x - 35
<em>Subtract 18x from both sides.</em>
-21/2x + 1/8 = -35
<em>Subtract 1/8 from both sides.</em>
-21/2x = -35 - 1/8
<em>-35 is the same as -280/8</em>.
-21/2x = (-280 - 1)/8
<em>Subtract 1 from -280 to get -281.</em>
-21/2x = -281/8
<em>Multiply both sides by -2/21 (reciprocal of -21/2).</em>
x = (-281 * -2)/(8 * 21)<em> </em>
<em>You can cross cancel -2 and 8</em> <em>by extracting 2 (they become -1 and 4 respectively).</em>
x = (-281 * -1)/(4 * 21)
<em>Multiply -281 by -1 to get 281.</em>
x = 281/(4 * 21)
<em>Multiply 4 by 21 to get 84.</em>
x = 281/84
<em>Can this fraction be simplified into a mixed number? Yes it can. It becomes 3 29/84. (252 (3 * 84) + 29 = 281)</em>
x = 3 29/84
Work check: x is substituted for 281/84 (convenience)
7 * 281/84 + 1/2(281/84 + 1/4) = 3((6 * 281)/84 - 9) - 8
1967/84 + 1/2(281/84 + 1/4) = 3((6 * 281)/84 - 9) - 8
1967/84 + 1/2(302/84) = 3((6 * 281)/84 - 9) - 8
(1967 + 151)/84 = 3((6 * 281)/84 - 9) - 8
2118/84 = 3(1686/84 - 9) - 8
2118/84 = 3((1686 - 756)/84) - 8
2118/84 = 3(930/84) - 8
2118/84 = 2790/84 - 672/84
2118/84 = (2790 - 672)/84
2118/84 = 2118/84
So x = 3 29/84 is correct.
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