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Solve for $x$: $\\displaystyle \\frac{a} {bx+c} + d= s$

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Rearrange the equation by adding {-c} to both sides to get:
\$\\simplify{{t} / ({a} * x + {b}) = {d} + { -c} = {d -c}}\$
This gives \$\\simplify{({a} * x + {b}) / {t} = 1 / {d -c}}\$ (this is because if $\\displaystyle \\frac{a}{b}=c$ then $\\displaystyle \\frac{b}{a}=\\frac{1}{c}$ on turning the fraction round the other way)
and so \$\\simplify{({a} * x + {b}) = {t} / {d -c}}\$ on multiplying both sides by {t}.
Hence \$\\simplify{{a} * x = {t} / {d -c} -{b} = ({a * an1} / {an2})}\$
and so \$\\simplify{x={an1}/{an2}}\$ is the solution on dividing both sides by {a}.

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

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Rearrange the equation by adding {-c} to both sides to get:
\$\\simplify[std]{{t} / ({a} * x + {b}) = {d} + { -c} = {d -c}}\$

\n\t\t\t\t\t

This gives \$\\simplify{({a} * x + {b}) / {t} = 1 / {d -c}}\$ (this is because if $\\displaystyle \\frac{a}{b}=c$ then $\\displaystyle \\frac{b}{a}=\\frac{1}{c}$ on turning the fraction round the other way)

\n\t\t\t\t\t

and so \$\\simplify{({a} * x + {b}) = {t} / {d -c}}\$ on multiplying both sides by {t}.

\n\t\t\t\t\t

Solve this equation for $x$.

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\$\\simplify{{t} / ({a} * x + {b}) + {c} = {d}}\$

\n\t\t\t

$x=\\;$ []

\n\t\t\t

If you want help in solving the equation, click on \"Show steps\". If you do so then you will lose 1 mark.

\n\t\t\t

Input all numbers as fractions or integers and not as decimals.

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Solve the following equation for $x$.

\n\t

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

\n\t \n\t \n\t \n\t \n\t"}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Timur Zaripov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3272/"}]}