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{"name": "Solving linear equations: one step: adding or subtracting ", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["a", "b", "ans1", "c", "d", "ans2", "g", "f", "ans3", "h", "j", "ans4"], "name": "Solving linear equations: one step: adding or subtracting ", "tags": ["algebra", "balancing equations", "Linear equations", "linear equations", "one step equations", "rearranging equations", "solving equations", "Solving equations"], "advice": "", "rulesets": {}, "parts": [{"stepsPenalty": "1", "prompt": "<p>Given $x+\\var{a}=\\var{b}$, we can rearrange the equation to that find $x=$&nbsp;[[0]].</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{ans1}", "minValue": "{ans1}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "<p>Given $x+\\var{a}=\\var{b}$, we subtract $\\var{a}$ from both sides to get $x$ by itself.</p>\n<p></p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: right;\">$x+\\var{a}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{b}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$x+\\var{a}-\\var{a}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{b}-\\var{a}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$x$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{ans1}$</td>\n</tr>\n</tbody>\n</table>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": 0, "showCorrectAnswer": true, "type": "gapfill"}, {"stepsPenalty": "1", "prompt": "<p>Given $y-\\var{c}=\\var{d}$, &nbsp;$y=$&nbsp;[[0]].</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{ans2}", "minValue": "{ans2}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "<p>Given $y-\\var{c}=\\var{d}$, we add $\\var{c}$ to both sides to get $y$ by itself.</p>\n<p></p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: right;\">$y-\\var{c}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{d}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$y-\\var{c}+\\var{c}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{d}+\\var{c}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$y$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{ans2}$</td>\n</tr>\n</tbody>\n</table>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": 0, "showCorrectAnswer": true, "type": "gapfill"}, {"stepsPenalty": "1", "prompt": "<p>Rearrange $\\var{f}+z=\\var{g}$ to determine the value of $z$.</p>\n<p>$z=$&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{ans3}", "minValue": "{ans3}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "<p>Given $\\var{f}+z=\\var{g}$, we subtract $\\var{f}$ from both sides to get $z$ by itself.</p>\n<p></p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: right;\">$\\var{f}+z$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{g}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\simplify[basic]{{f}+z-{f}}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\simplify[basic]{{g}-{f}}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$z$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{ans3}$</td>\n</tr>\n</tbody>\n</table>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": 0, "showCorrectAnswer": true, "type": "gapfill"}, {"stepsPenalty": "1", "prompt": "<p>Solve $\\var{h}=\\var{j}+a$ for $a$.</p>\n<p>$a=$&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{ans4}", "minValue": "{ans4}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "<p>Given $\\var{h}=\\var{j}+a$, we subtract $\\var{j}$ from both sides to get $a$ by itself.</p>\n<p></p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: right;\">$\\var{h}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{j}+a$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\simplify[basic]{{h}-{j}}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\simplify[basic]{{j}+a-{j}}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\var{ans4}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$a$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$a$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{ans4}$</td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, 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