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Input as a fraction or an integer, not as a decimal.

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\\[\\simplify{{a} * x + {b} = {c} * x + {d}}\\]

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$x=\\;$ [[0]]

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Solve the following equation for $x$.

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Input your answer as a fraction or an integer as appropriate and not as a decimal.

\n \n ", "tags": ["algebra", "algebraic fractions", "algebraic manipulation", "changing the subject of an equation", "checked2015", "rearranging equations", "SFY0001", "solving", "solving equations", "Solving equations", "subject of an equation"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"notes": "\n \t\t \t\t\t\t\t\t \t\t \t\t\t\t \n \t\t", "licence": "Creative Commons Attribution 4.0 International", "description": "

Solve for $x$: $\\displaystyle ax+b = cx+d$

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If $\\simplify{{a}*x + {b}}=\\simplify{{c}*x + {d}}$, then we first subtract $\\var{c}x$ from each side.

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We obtain $\\simplify{{a}x - {c}x+ {b}}= \\var{d}$.

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Next we subtract $\\var{b}$ from each side (or add $\\var{-b}$ if you prefer - it means the same thing), to obtain $\\var{a}x - \\var{c}x = \\simplify{{d}-{b}}$.

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In other words $\\simplify{{a}-{c}}x= \\simplify{{d}-{b}}$.

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Now divide both sides by $\\simplify{{a-c}}$ to obtain $x=\\dfrac{\\simplify{{d-b}}}{\\simplify{{a-c}}}$ $=\\Large{\\simplify{{an1}/{an2}}}$.

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