Covering 1-3 step linear equations but not introducing brackets or an unknown on both sides.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", "", "", ""], "variable_overrides": [[], [], [], [], [], []], "questions": [{"name": "37.a Simple linear equations 1 - Just addition", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}], "tags": [], "metadata": {"description": "One-step equation solving - just adding.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "Solve the following equation for $\\var{Letter}$.
\n\\[\\simplify{{Letter}+{Num1}}=\\var{Num2}.\\]
", "advice": "To solve $\\simplify{{Letter}+{Num1}}=\\var{Num2}$ we need to get the $\\var{Letter}$ by itself. We need to get rid of the $\\var{Num1}$ so if we add $\\var{-Num1}$ to both sides then we will get the $\\var{Letter}$ by itself. This gives us
\n\\[\\simplify{{Letter}+{Num1}}=\\var{Num2}\\]
\n\\[\\simplify[basic]{{Letter}+{Num1}+{-Num1}}=\\simplify[basic]{{Num2}+{-Num1}}\\]
\n\\[\\var{Letter}+0=\\var{Num2-Num1}\\]
\n\\[\\var{Letter}=\\var{Num2-Num1}.\\]
\n
Use this link to find resources to help you revise how to solve linear equations
$\\var{Letter}=$
", "minValue": "{Num2-Num1}", "maxValue": "{Num2-Num1}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "37.b Simple linear equations 2 - Just division", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}], "tags": [], "metadata": {"description": "One step equations - just division.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "Solve the following equation for $\\var{Letter}$.
\n\\[\\simplify{{Num1}{Letter}}=\\var{Num2*Num1}.\\]
", "advice": "To solve $\\simplify{{Num1}{Letter}}=\\var{Num2*Num1}$ we need to get the $\\var{Letter}$ by itself. We need to get rid of the $\\var{Num1}$ so if we divide by $\\var{Num1}$ on both sides then we will get the $\\var{Letter}$ by itself. This gives us
\n\\[\\simplify{{Num1}{Letter}}=\\var{Num2*Num1}\\]
\n\\[\\simplify{{Num1}{Letter}}\\div\\var{Num1}=\\var{Num2*Num1}\\div\\var{Num1}\\]
\n\\[1\\times\\var{Letter}=\\var{Num2}\\]
\n\\[\\var{Letter}=\\var{Num2}.\\]
\n
Use this link to find resources to help you revise how to solve linear equations
$\\var{Letter}=$
", "minValue": "{Num2}", "maxValue": "{Num2}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "37.c Simple linear equations 3 - Just multiplication", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}], "tags": [], "metadata": {"description": "One step equations - just multiplication.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "Solve the following equation for $\\var{Letter}$.
\n\\[\\frac{\\var{Letter}}{\\var{Num1}}=\\var{Num2}.\\]
", "advice": "To solve $\\frac{\\var{Letter}}{\\var{Num1}}=\\var{Num2}$ we need to get the $\\var{Letter}$ by itself. We need to get rid of the $\\var{Num1}$ so if we multiply by $\\var{Num1}$ on both sides then we will get the $\\var{Letter}$ by itself. This gives us
\n\\[\\frac{\\var{Letter}}{\\var{Num1}}=\\var{Num2}\\]
\n\\[\\frac{\\var{Letter}}{\\var{Num1}}\\times\\var{Num1}=\\var{Num2}\\times\\var{Num1}\\]
\n\\[\\var{Letter}=\\var{Num2*Num1}.\\]
\n
Use this link to find resources to help you revise how to solve linear equations
$\\var{Letter} =$
", "minValue": "{Num1*Num2}", "maxValue": "{Num1*Num2}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "37.d Simple linear equations 4 - Addition and division", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}], "tags": [], "metadata": {"description": "Solving two step equations.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "Solve the following equation for $\\var{Letter}$.
\n\\[\\simplify[basic]{{Num1}{Letter}+{Num2}}=\\var{Num3*Num1+Num2}.\\]
", "advice": "To solve $\\simplify[basic]{{Num1}{Letter}+{Num2}}=\\var{Num3*Num1+Num2}$ we need to get the $\\var{Letter}$ by itself. If we divide both sides by $\\var{Num1}$ then we would need to divide both $\\var{Num2}$ and $\\var{Num3*Num1+Num2}$ so it will be easier to deal with $\\var{Num2}$ first by subtracting it from both sides and then dividing by $\\var{Num1}$ afterwards. This gives us the following,
\n\\[\\simplify[basic]{{Num1}{Letter}+{Num2}}=\\var{Num3*Num1+Num2}\\]
\n\\[\\simplify[basic]{{Num1}{Letter}+{Num2}-{Num2}}=\\simplify[basic]{{Num3*Num1+Num2}-{Num2}}\\]
\n\\[\\simplify[basic]{{Num1}{Letter}}=\\var{Num3*Num1}\\]
\n\\[\\simplify[basic]{{Num1}{Letter}}\\div\\var{Num1}=\\var{Num3*Num1}\\div\\var{Num1}\\]
\n\\[\\var{Letter}=\\var{Num3}.\\]
\n
Use this link to find resources to help you revise how to solve linear equations
$\\var{Letter} =$
", "minValue": "{Num3}", "maxValue": "{Num3}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "37.e Simple linear equations 5 - Addition and multiplication", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}], "tags": [], "metadata": {"description": "Solving two step linear equations including a division.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "Solve the following equation for $\\var{Letter}$.
\n\\[\\simplify[basic]{{Letter}/{Num1}+{Num2}}=\\var{Num3}.\\]
", "advice": "To solve $\\simplify[basic]{{Letter}/{Num1}+{Num2}}=\\var{Num3}$ we need to get the $\\var{Letter}$ by itself. It is easiest if we subtract $\\var{Num2}$ from both sides first but it would also be ok to multiply both sides by $\\var{Num1}$ so long as we remember to multiply both $\\simplify[basic]{{Letter}/{Num1}}$ and $\\var{Num2}$. Starting by subtracting $\\var{Num2}$ from both sides we get the following.
\n\\[\\simplify[basic]{{Letter}/{Num1}+{Num2}}=\\var{Num3}\\]
\n\\[\\simplify[basic]{{Letter}/{Num1}+{Num2}-{Num2}}=\\simplify[basic]{{Num3}-{Num2}}\\]
\n\\[\\simplify[basic]{{Letter}/{Num1}}=\\var{Num3-Num2}\\]
\n\\[\\simplify[basic]{{Letter}/{Num1}}\\times \\var{Num1}=\\var{Num3-Num2}\\times\\var{Num1}\\]
\n\\[\\var{Letter}=\\var{(Num3-Num2)*Num1}.\\]
\n
Use this link to find resources to help you revise how to solve linear equations
$\\var{Letter} =$
", "minValue": "{Num1*(Num3-Num2)}", "maxValue": "{Num1*(Num3-Num2)}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "37.f Simple linear equations 6 - Addition, multiplication, and division", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}], "tags": [], "metadata": {"description": "Solving three step linear equations.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "Solve the following equation for $\\var{Letter}$.
\n\\[\\simplify[basic]{({Num1}{Letter}+{Num2*Num1})/{Num3}}=\\var{Num4*Num1}.\\]
", "advice": "To solve $\\simplify[basic]{({Num1}{Letter}+{Num2*Num1})/{Num3}}=\\var{Num4*Num1}$ we need to get the $\\var{Letter}$ by itself. We need to remember BIDMAS to know which numbers to move across first. Remember we treat the top of a fraction like it is in brackets.
\n\\[\\simplify[basic]{({Num1}{Letter}+{Num2*Num1})/{Num3}}=\\var{Num4*Num1}\\]
\n\\[\\simplify[basic]{({Num1}{Letter}+{Num2*Num1})/{Num3}}\\times\\var{Num3}=\\var{Num4*Num1}\\times\\var{Num3}\\]
\n\\[\\simplify[basic]{{Num1}{Letter}+{Num2*Num1}}=\\var{Num4*Num1*Num3}\\]
\n\\[\\simplify[basic]{{Num1}{Letter}+{Num2*Num1}-{Num2*Num1}}=\\simplify[basic]{{Num4*Num1*Num3}-{Num2*Num1}}\\]
\n\\[\\simplify[basic]{{Num1}{Letter}}=\\var{Num4*Num1*Num3-Num2*Num1}\\]
\n\\[\\simplify[basic]{{Num1}{Letter}}\\div\\var{Num1}=\\var{Num4*Num1*Num3-Num2*Num1}\\div\\var{Num1}\\]
\n\\[\\var{Letter}=\\var{Num4*Num3-Num2}.\\]
\n
Use this link to find resources to help you revise how to solve linear equations
$\\var{Letter} =$
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