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Solve a simple linear equation algebraically. The unknown appears on both sides of the equation.
", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "Consider the equation \\[ \\var{d}x-\\var{f}=\\var{g}x+\\var{h} \\]
", "advice": "We are asked to solve the equation
\n\\[ \\var{d}x-\\var{f}=\\var{g}x+\\var{h} \\]
\nIn this equation, there are $x$ terms and constant terms on both sides of the equals sign.
\nTo solve this equation, we must rearrange it to get $x$ on its own.
\n\\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}
What is the value of $x$?
\n$x = $ [[0]]
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