Solve linear equations with unknowns on one. Including brackets and fractions. Solutions may require rounding.
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\nThe first step is to isolate all the $x$-terms to one side of the equation.
\nTo do that we will {add} $\\var{abs(b)}$ {tofroma} both sides:
\n\\[ \\begin{split} \\simplify{{a}x + {b}} = {{ \\end{split} \\]
\nNow we need to divide both sides by the coefficient of $x$, to leave just one $x$.
\nDividing both sides by $\\var{a}$,
\n\\[ \\begin{split} x &= \\frac{\\simplify{{c}-{b}}}{\\var{a}} \\\\ &=\\simplify{{(c-b)/a}} \\end{split}\\]
\nRounding your answer as required,
\\[ x = \\var{precround((c-b)/a,2)} \\]
\\[ \\frac{\\simplify{{d}x + {f}}}{\\var{g}} = \\var{h} \\]
The first step is to rearrange by removing the fraction on the left. To do this we mulitply both sides by $\\var{g}$ :
\\[ \\begin{split} \\frac{\\simplify{{d}x + {f}}}{\\var{g}} \\times \\var{g} &= \\var{h} \\times \\var{g} \\\\\\\\ \\simplify{{d}x + {f}} &= \\var{h*g} \\end{split} \\]
Next we isolate all the $x$-terms to one side of the equation.
To do that we will {add2} $\\var{abs(f)}$ {tofromb} both sides:
\\[ \\begin{split} \\simplify{{d}x + {f}} \\var{add2sym} \\var{abs(f)} &= \\var{h*g} \\var{add2sym} \\var{abs(f)} \\\\
\\var{d}x &= \\simplify{{h*g}-{f}} \\end{split} \\]
Finally we need to divide both sides by the coefficient of $x$, to leave just one $x$.
Dividing both sides by $\\var{d}$,
\\[ \\begin{split} x &= \\frac{\\simplify{{h*g}-{f}}}{\\var{d}} \\\\ &= \\var{(h*g-f)/d} \\end{split} \\]
Rounding your answer as required,
\n\\[ x = \\var{precround((h*g-f)/d,2)} \\]
\n\n\\[ \\simplify{{b}({c}x+{g})} = \\var{d} \\]
\nEven though this looks different, this is quite similar to part b). We just have a multiplication rather than a division to deal with as the first step.
Rearrange to remove the multiplication on the left. To do this we divide both sides by $\\var{b}$:
\\[ \\begin{split} \\frac{\\simplify{{b}({c}x+{g})}}{ \\var{b}} &= \\frac{\\var{d}}{\\var{b}} \\\\ \\\\ \\simplify{{c}x+{g}} &= \\var{precround(d/b,3)} \\end{split} \\]
Do the division on the right with a calculator and round to 3 decimal places. Always use at least one more decimal place when rounding during the calculation than is required in your answer, to be on the safe side.
Next we isolate all the $x$-terms to one side of the equation.
To do that we will {add3} $\\var{abs(g)}$ {tofromc} both sides:
\\[ \\begin {split} \\simplify{{c}x + {g}} \\var{add3sym} \\var{abs(g)} &= \\var{precround(d/b,3)} \\var{add3sym} \\var{abs(g)} \\\\ \\var{c}x &= \\var{precround(d/b - g,3)} \\end{split} \\]
Finally we need to divide both sides by the coefficient of $x$, to leave just one $x$
Dividing both sides by $\\var{c}$:
\\[ \\begin{split} x &= \\frac{\\var{precround(d/b - g,3)}}{\\var{c}} \\\\ &= \\var{(d/b-g)/c} \\end{split} \\]
Rounding your answer as required,
\\[ x = \\var{precround((d/b - g)/c,2)} \\]
Solve
\n$\\simplify{{a}x + {b}} = \\var{c}$
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\n$\\dfrac{\\simplify{{d}x + {f}}}{\\var{g}} = \\var{h}$
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\n$\\simplify{{b}({c}x+{g})} = \\var{d}$
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