Answer: x = 8/3 ; or, write as: 2 2/3; or, write as, 2.66666667 .
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Explanation:
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Given: 5 − 1/2 x = 5/8 x + 2 ;
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Change the 1/2 x to "4/8 x" ;
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Since "1/2" = "(1*4)/(2*4)" = "(4/8)"; and rewrite:
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→ 5 − (4/8)x = (5/8)x + 2 ;
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Subtract "5"; and add "(5/8)x" to EACH side of the equation:
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5 − (4/8)x − 5 + (5/8)x = (5/8)x + 2 − 5 + (5/8)x ;
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to get:
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(1/8) x = (10/8)x − 3
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Multiply the entire equation (BOTH SIDES) by "8"; to get rid of the fraction:
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8 * { (1/8) x = (10/8)x − 3 };
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to get:
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x = 10x − 24 ;
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Subtract "x" ; and add "24" ; to EACH side of the equation:
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→ x − x + 24 = 10x − 24 − x + 24 ;
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to get:
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→ 24 = 9x ; ↔ 9x = 24 ;
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→ Divide EACH side of the equation by "9" ; to isolate "x" on one side of the equation; and to solve for "x" ;
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→ 9x / 9 = 24 / 9 ;
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→ x = 24/9 = (24÷3)/ (9÷3) = 8/3
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→ x = 8/3 ; or, write as: 2 2/3; or, write as, 2.66666667.
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