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Solve a simple linear equation algebraically. The unknown appears on both sides of the equation.

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We are asked to solve the equation

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\$\\var{d}x-\\var{f}=\\var{g}x+\\var{h} \$

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In this equation, there are $x$ terms and constant terms on both sides of the equals sign.

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To solve this equation, we must rearrange it to get $x$ on its own.

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\\begin{align}
\\var{d}x-\\var{f} &= \\var{g}x+\\var{h} \\\\[0.5em]
\\var{d}x-\\var{g}x &= \\var{h}+\\var{f} & \\text{Move } x \\text{ terms to the left, and constant terms to the right.}\\\\[0.5em]
\\simplify{{d-g}*x} &= {\\var{h+f}} & \\text{Collect like terms together.}\\\\[0.5em]
x &=\\frac{\\var{h+f}}{\\var{d-g}} & \\text{Divide both sides by } \\var{d-g} \\text{.} \\\\[0.5em]
x &= \\simplify{{h+f}/{d-g}}
\\end{align}

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$\\var{d}x-\\var{f}=\\var{g}x+\\var{h}$

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What is the value of $x$?

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$x =$ [[0]]

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