// Numbas version: exam_results_page_options {"name": "Rachel's copy of Algebra VI: Solving Linear Equations (Sarah)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variables": {"ans4": {"templateType": "anything", "definition": "n*m+l", "description": "", "group": "Ungrouped variables", "name": "ans4"}, "f": {"templateType": "anything", "definition": "random(2..12)", "description": "", "group": "Ungrouped variables", "name": "f"}, "q": {"templateType": "anything", "definition": "random(-12..12 except [0,1,-1])", "description": "", "group": "Ungrouped variables", "name": "q"}, "p": {"templateType": "anything", "definition": "random(-12..12 except[0,q])", "description": "", "group": "Ungrouped variables", "name": "p"}, "ans3": {"templateType": "anything", "definition": "(k+j)*h", "description": "", "group": "Ungrouped variables", "name": "ans3"}, "r": {"templateType": "anything", "definition": "random(1..12)", "description": "", "group": "Ungrouped variables", "name": "r"}, "m": {"templateType": "anything", "definition": "random(2..12 except l)", "description": "", "group": "Ungrouped variables", "name": "m"}, "s": {"templateType": "anything", "definition": "random([-13,-11,-7,-5,-3,-2,13,11,7,5,3,2])", "description": "", "group": "Ungrouped variables", "name": "s"}, "l": {"templateType": "anything", "definition": "random(2..12)", "description": "", "group": "Ungrouped variables", "name": "l"}, "g": {"templateType": "anything", "definition": "random(-12..12 except [0])", "description": "", "group": "Ungrouped variables", "name": "g"}, "b": {"templateType": "anything", "definition": "random(2..12 except a)", "description": "", "group": "Ungrouped variables", "name": "b"}, "ans6": {"templateType": "anything", "definition": "u*t/s", "description": "", "group": "Ungrouped variables", "name": "ans6"}, "a": {"templateType": "anything", "definition": "random(2..12)", "description": "", "group": "Ungrouped variables", "name": "a"}, "n": {"templateType": "anything", "definition": "random(-12..12)", "description": "", "group": "Ungrouped variables", "name": "n"}, "ans2": {"templateType": "anything", "definition": "(g-d)/(-f)", "description": "", "group": "Ungrouped variables", "name": "ans2"}, "c": {"templateType": "anything", "definition": "random(-12..12 except [0,b])", "description": "", "group": "Ungrouped variables", "name": "c"}, "ans5": {"templateType": "anything", "definition": "p/q-r", "description": "", "group": "Ungrouped variables", "name": "ans5"}, "j": {"templateType": "anything", "definition": "random(2..12 except [h])", "description": "", "group": "Ungrouped variables", "name": "j"}, "t": {"templateType": "anything", "definition": "random([13,11,7,5,3,2] except s)", "description": "", "group": "Ungrouped variables", "name": "t"}, "k": {"templateType": "anything", "definition": "random(-13..-1 except -j)", "description": "", "group": "Ungrouped variables", "name": "k"}, "u": {"templateType": "anything", "definition": "random(-12..12 except 0)", "description": "", "group": "Ungrouped variables", "name": "u"}, "ans1": {"templateType": "anything", "definition": "(c-b)/a", "description": "", "group": "Ungrouped variables", "name": "ans1"}, "d": {"templateType": "anything", "definition": "random(1..12 except [f,g])", "description": "", "group": "Ungrouped variables", "name": "d"}, "h": {"templateType": "anything", "definition": "random(list(2..12)+[20,50,100,200])", "description": "", "group": "Ungrouped variables", "name": "h"}}, "functions": {}, "tags": [], "statement": "

Solve the following equations for x:

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Part a)

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Given $\\var{a}x+\\var{b}=\\var{c}$, we can start by subtracting $\\var{b}$ from both sides to get $\\var{a}x = \\simplify{{c-b}}$.

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Dividing both sides by $\\var{a}$ gives us $x= \\simplify {{c-b}/{a}}$

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Part b)

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We could start by subtracting $\\var{d}$ from both sides to get $-\\var{f}y = \\simplify{{g-d}}$.

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Or we could first add $\\var{f}y$ to both sides to get $\\var{d} = \\var{g} + \\var{f}y$. This avoids needing to divide by a negative number.

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Either way we should end up with $y= \\dfrac{\\simplify{{d- g}}}{\\var{f}}= \\simplify{{d-g}/{f}}$.

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Part c)

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$\\displaystyle{\\frac{z}{\\var{h}}}-\\var{j}=\\var{k}$

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$\\displaystyle{\\frac{z}{\\var{h}}}=\\var{k+j}$

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$z=\\var{ans3}$

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Part d)

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$\\displaystyle{\\frac{a-\\var{l}}{\\var{m}}}=\\var{n}$

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$a-\\var{l}=\\var{n*m}$

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$a=\\var{ans4}$

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Part e)

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$\\var{p}$$=$$\\var{q}(\\var{r}+b)$

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$\\displaystyle{\\simplify{{p}/{q}}}$$=$$\\var{r}+b$

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$\\displaystyle{\\simplify{{p-r*q}/{q}}}$$=$$b$

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Part f)

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$\\displaystyle{\\frac{\\var{s}w}{\\var{t}}}$$=$$\\var{u}$

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$\\var{s}w$$=$$\\var{u*t}$

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$w$$=$$\\displaystyle{\\simplify{{u*t}/{s}}}$

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For more help, check this video-

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$\\var{a}x+\\var{b}=\\var{c}$

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$x=$ [[0]].

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• In order to solve for the unknown variable, you must isolate the variable.
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• In the order of operation, multiplication and division are completed before addition and subtraction.
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Example:   5 x - 6 = 3 x - 8

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Subtract 3x from both sides of the equation: 2x - 6 = -8

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Add 6 to both sides of the equation: 2x = -2 or x= -1

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$\\var{d}-\\var{f}y=\\var{g}$

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$y=$ [[0]].

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\n
• In order to solve for the unknown variable, you must isolate the variable.
• \n
• In the order of operation, multiplication and division are completed before addition and subtraction.
• \n
", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showFeedbackIcon": true, "type": "information", "scripts": {}}]}, {"stepsPenalty": 0, "marks": 0, "prompt": "

$\\displaystyle{\\frac{z}{\\var{h}}}-\\var{j}=\\var{k}$

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$z=$ [[0]]

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\n
• In order to solve for the unknown variable, you must isolate the variable.
• \n
• In the order of operation, multiplication and division are completed before addition and subtraction.
• \n
", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showFeedbackIcon": true, "type": "information", "scripts": {}}]}, {"stepsPenalty": 0, "marks": 0, "prompt": "

$\\displaystyle{\\frac{a-\\var{l}}{\\var{m}}}=\\var{n}$.

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$a=$ [[0]]

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\n
• In order to solve for the unknown variable, you must isolate the variable.
• \n
• In the order of operation, multiplication and division are completed before addition and subtraction.
• \n
", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showFeedbackIcon": true, "type": "information", "scripts": {}}]}, {"stepsPenalty": 0, "marks": 0, "prompt": "

$\\var{p}=\\var{q}(\\var{r}+b)$.

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$b=$ [[0]]

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\n
• In order to solve for the unknown variable, you must isolate the variable.
• \n
• In the order of operation, multiplication and division are completed before addition and subtraction.
• \n
", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showFeedbackIcon": true, "type": "information", "scripts": {}}]}, {"stepsPenalty": 0, "marks": 0, "prompt": "

$\\displaystyle{\\frac{\\var{s}w}{\\var{t}}}=\\var{u}$.

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$w=$ [[0]]

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\n
• In order to solve for the unknown variable, you must isolate the variable.
• \n
• In the order of operation, multiplication and division are completed before addition and subtraction.
• \n
", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showFeedbackIcon": true, "type": "information", "scripts": {}}]}], "extensions": [], "variable_groups": [], "name": "Rachel's copy of Algebra VI: Solving Linear Equations (Sarah)", "metadata": {"description": "

This exercise will help you solve equations of type ax-b = c.

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