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Input your answer as a fraction or an integer. Do not input the answer as a decimal. 

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\\[\\simplify[std]{{a} * x + {b} = {c} * x + {d}}\\]
Input your answer as a fraction or an integer. Do NOT input the answer as a decimal.

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

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Solve the following linear equation for $x$.

", "tags": ["checked2015", "equations", "linear equation", "mas1601", "MAS1601", "solving equations", "Solving equations", "solving linear equations"], "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers"]}, "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"notes": "

5/08/2012:

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Added more tags.

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Added description.

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Checked calculation. OK.

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

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Given the equation \\[\\simplify[std]{{a}x+{b}={c}x+{d}}\\] we first collect together all the constant terms, and collect together all the terms in $x$.

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The equation can then be written as:
\\[\\simplify[std]{({a}-{c})x=({d}+{-b})}\\] i.e.
\\[\\simplify{{a-c}x={d-b}}\\]
which gives \\[x =\\simplify[std]{{(d-b)}/{(a-c)}}\\] as the solution.

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