A summary of the fourth week of material.
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", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "", "advice": "Given $\\simplify{{m}w-{n} = {p}w+{q}}$, we can get all the $w$'s on the left hand side and all the numbers on the right hand side, and then divide both sides by the coefficient of $w$ to get $w$ by itself.
\n\n| \n | \n | \n |
| \n | \n | \n |
| $\\simplify{{m}w+{n}}$ | \n$=$ | \n$\\simplify{{p}w+{q}}$ | \n
| \n | \n | \n |
| $\\simplify[!cancelTerms,unitFactor]{{m}w-{n}-{p}w}$ | \n$=$ | \n$\\simplify[!cancelTerms,unitFactor]{{p}w+{q}-{p}w}$ | \n
| \n | \n | \n |
| $\\simplify{{m-p}w-{n}}$ | \n$=$ | \n$\\var{q}$ | \n
| \n | \n | \n |
| $\\var{m-p}w-\\var{n}+\\var{n}$ | \n$=$ | \n$\\var{q}+\\var{n}$ | \n
| \n | \n | \n |
| $\\var{m-p}w$ | \n$=$ | \n$\\var{q+n}$ | \n
| \n | \n | \n |
| $\\displaystyle{\\frac{\\var{m-p}w}{\\var{m-p}}}$ | \n$=$ | \n$\\displaystyle{\\frac{\\var{q+n}}{\\var{m-p}}}$ | \n
| \n | \n | \n |
| $w$ | \n$=$ | \n$\\displaystyle{\\simplify{{q+n}/{m-p}}} = \\var{precround(ansA,1)} \\text{ to 1 dp}$ | \n
Use this link to find resources to help you revise how to solve linear equations
Solve $\\simplify{({m}w-{n}) = {p}w+{q}}$
\n$w=$ [[0]]
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", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "", "advice": "\nTo solve an equation like
\n$\\displaystyle{\\frac{x+\\var{num1}}{\\var{num2}}+\\frac{x}{\\var{num3}}=\\var{num4}},$
\nthe first thing to deal with is the denominators of the fractions. In order to do that you multiply both sides of the equation by both denominators $\\var{num2}$ and $\\var{num3}$ (or their lowest common multiple to be slightly more efficient). This will give something equivalent to:
\n$\\displaystyle{\\var{num3 + num2} x+\\var{num3*num1} = \\var{num2*num3*num4}.}$
\nThen proceeding by subtracting $\\var{num3*num1} from both sides:
\n$\\displaystyle{\\var{num3 + num2} x = \\var{num2*num3*num4-num3*num1}.}$
\nAnd finally dividing by $\\var{num2+num3}$:
\n$\\displaystyle{x = \\frac{\\var{num2*num3*num4-num3*num1}}{\\var{num2+num3}}.}$
\n
Use this link to find resources to help you revise how to solve linear equations
Solve $\\displaystyle{\\frac{x+\\var{num1}}{\\var{num2}}+\\frac{x}{\\var{num3}}=\\var{num4}}$.
\n$x=$ [[0]]
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", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "Rearrange the following equation, to make $y$ the subject:
\n\\[{cy -b = 3x}\\]
", "advice": "In order to rearrange the equation so that it is in terms of $y$, we must first add $b$ to both sides, and then divide both sides of the equation by $c$:
\n\\begin{split} cy-b &= 3x \\\\ cy &= 3x + b \\\\ y &=\\frac{3x+b}{c} \\end{split}
\n\nUse this link to find some resources which will help you revise this topic.
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\nRearranging algebraic formulae
\nIn the answers to each question you can find links to materials through the MaSH website to help you study those topics.
\nYou can always contact the Maths and Stats Help team (MaSH) to arrange a one to one appointment or check out our workshop timetable to see if you can access the support you need that way.
\nFind all this information via our website here!
", "end_message": "Thanks for completing this quiz. Don't forget to check out the MaSH resources on their website here.
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