$\\simplify{y={c[0]}x+{c[1]}}$
\n$x=$ [[0]]
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\n$x=$ [[0]]
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\n$x=$ [[0]]
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\n$x=$ [[0]]
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\n$x=$ [[0]]
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", "preamble": {"js": "", "css": ""}, "variablesTest": {"maxRuns": 100, "condition": ""}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "Rearranging equations to change the subject
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\n$\\simplify{y={c[0]}x+{c[1]}}$
\n$\\simplify{y-{c[1]}={c[0]}x}$
\n$\\simplify{(y-{c[1]})/{c[0]}={x}}$ (dividing both sides by $\\var{c[0]}$)
\n\n(b)
\n$\\simplify{y={c[2]}x/({c[3]}+x)}$
\n$\\simplify{y*({c[3]}+x)={c[2]}}x$ (multiply both sides by denominator)
\n$\\simplify{y*{c[3]}+x y={c[2]}}x$ (expanding bracket)
\n$\\simplify{y*{c[3]}={c[2]}x- y x}$ (moving all $x$ to the same side)
\n$\\simplify{y*{c[3]}=x({c[2]}- y)}$ (factorising)
\n$\\simplify{(y*{c[3]})/({c[2]}- y)=x}$
\n\n(c)
\n$\\simplify{y={c[7]}-{c[8]}/({c[9]}+x)}$
\n$\\simplify{y-{c[7]}=-{c[8]}/({c[9]}+x)}$
\n$\\simplify{({c[9]}+x)=-{c[8]}/(y-{c[7]})}$
\n$\\simplify{x=-{c[9]}-{c[8]}/(y-{c[7]})}$ which is algebraically the same as $\\simplify{x=(-{c[9]}(y-{c[7]})-{c[8]})/(y-{c[7]})}=\\simplify{(-{c[9]}y+{c[7]*c[9]-c[8]})/(y-{c[7]})}$
\n\n(d)
\n$\\simplify{y=sqrt(x+{c[10]})}$
\n$\\simplify{y^2=(x+{c[10]})}$ (squaring both sides)
\n$\\simplify{y^2-{c[10]}=x}$
\n\n(e)
\n$\\simplify{y=1/x+{c[11]}}$
\n$\\simplify{y-{c[11]}=1/x}$
\n$\\simplify{x(y-{c[11]})=1}$ (multiply both sides by $x$)
\n$\\simplify{x=1/(y-{c[11]})}$
", "type": "question", "contributors": [{"name": "Katie Lester", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/586/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}]}], "contributors": [{"name": "Katie Lester", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/586/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}