{"questions":[{"content":"Используя распределительное свойство умножения, упростите выражение $$(78-x)\\cdot4=$$[[choice-1]]","widgets":{"choice-1":{"type":"choice","options":["$78\\cdot4-4x$","$4x-78\\cdot4$","$78\\cdot x-4x$"],"answer":[0]}},"step":1,"hints":["$(\\textcolor{coral}{a}-\\textcolor{green}{b})\\cdot \\textcolor{blue}{c}=\\textcolor{coral}{a}\\textcolor{blue}{c}-\\textcolor{green}{b}\\textcolor{blue}{c}$","$(\\textcolor{coral}{78}-\\textcolor{green}{x})\\cdot \\textcolor{blue}{4}=\\textcolor{coral}{78}\\cdot \\textcolor{blue}{4}-\\textcolor{green}{4}\\textcolor{blue}{x}$"],"id":"0"},{"content":"Используя распределительное свойство умножения, упростите выражение $$(x-13)\\cdot15=$$[[choice-8]]","widgets":{"choice-8":{"type":"choice","options":["$15x-13\\cdot15$","$13x-15x$","$13\\cdot15-15x$"],"answer":[0]}},"step":1,"hints":["$(\\textcolor{coral}{a}-\\textcolor{green}{b})\\cdot \\textcolor{blue}{c}=\\textcolor{coral}{a}\\textcolor{blue}{c}-\\textcolor{green}{b}\\textcolor{blue}{c}$","$(\\textcolor{coral}{x}-\\textcolor{green}{13})\\cdot \\textcolor{blue}{15}=\\textcolor{blue}{15}\\textcolor{coral}{x}-\\textcolor{green}{13}\\cdot \\textcolor{blue}{15}$"],"id":"0"},{"content":"Используя распределительное свойство умножения, упростите выражение $$(x+53)\\cdot6=$$[[choice-24]]","widgets":{"choice-24":{"type":"choice","options":["$6x+53\\cdot6$","$6x-53\\cdot6$","$53x+6\\cdot53$"],"answer":[0]}},"step":1,"hints":["$(\\textcolor{coral}{a}+\\textcolor{green}{b})\\cdot \\textcolor{blue}{c}=\\textcolor{coral}{a}\\textcolor{blue}{c}+\\textcolor{green}{b}\\textcolor{blue}{c}$","$(\\textcolor{coral}{x}+\\textcolor{green}{53})\\cdot \\textcolor{blue}{6}=\\textcolor{blue}{6}\\textcolor{coral}{x}+\\textcolor{green}{53}\\cdot \\textcolor{blue}{6}$"],"id":"0"},{"instruction":"Упростите выражение","content":"$11x+12x=$[[choice-49]]","widgets":{"choice-49":{"type":"choice","options":["$23x$","$13x$","$23$"],"answer":[0]}},"step":1,"hints":["Распределительное свойство умножения работает и в обратную сторону: $$\\textcolor{coral}{a}\\textcolor{blue}{c}+\\textcolor{green}{b}\\textcolor{blue}{c}=(\\textcolor{coral}{a}+\\textcolor{green}{b})\\cdot \\textcolor{blue}{c}$$","$\\textcolor{coral}{11}\\textcolor{blue}{x}+\\textcolor{green}{12}\\textcolor{blue}{x}=(\\textcolor{coral}{11}+\\textcolor{green}{12})\\cdot \\textcolor{blue}{x}=23\\textcolor{blue}{x}$"],"id":"1"},{"instruction":"Упростите выражение","content":"$15x+17x=$[[choice-83]]","widgets":{"choice-83":{"type":"choice","options":["$32x$","$27x$","$33$"],"answer":[0]}},"step":1,"hints":["Распределительное свойство умножения работает и в обратную сторону: $$\\textcolor{coral}{a}\\textcolor{blue}{c}+\\textcolor{green}{b}\\textcolor{blue}{c}=(\\textcolor{coral}{a}+\\textcolor{green}{b})\\cdot \\textcolor{blue}{c}$$","$\\textcolor{coral}{15}\\textcolor{blue}{x}+\\textcolor{green}{17}\\textcolor{blue}{x}=(\\textcolor{coral}{15}+\\textcolor{green}{17})\\cdot \\textcolor{blue}{x}=32\\textcolor{blue}{x}$"],"id":"1"},{"instruction":"Упростите выражение","content":"$26x-16x=$[[choice-126]]","widgets":{"choice-126":{"type":"choice","options":["$10x$","$11x$","$11$"],"answer":[0]}},"step":1,"hints":["Распределительное свойство умножения работает и в обратную сторону: $$\\textcolor{coral}{a}\\textcolor{blue}{c}-\\textcolor{green}{b}\\textcolor{blue}{c}=(\\textcolor{coral}{a}-\\textcolor{green}{b})\\cdot \\textcolor{blue}{c}$$","$\\textcolor{coral}{26}\\textcolor{blue}{x}-\\textcolor{green}{16}\\textcolor{blue}{x}=(\\textcolor{coral}{26}-\\textcolor{green}{16})\\cdot \\textcolor{blue}{x}=10\\textcolor{blue}{x}$"],"id":"1"},{"instruction":"Упростите выражение","content":"$7y+14-3y$[[choice-184]]","widgets":{"choice-184":{"type":"choice","options":["$4y+14$","$18$","$7y+17$"],"answer":[0]}},"step":1,"hints":["Cгруппируем члены выражения, содержащие $y$:$$(7y-3y)+14$$","Применим распределительное свойство умножения и выполним расчет:$$(7-3)y + 14\\newline4y+14$$"],"id":"2"},{"instruction":"Упростите выражение","content":"$4y+17+16y$[[choice-266]]","widgets":{"choice-266":{"type":"choice","options":["$20y+17$","$37$","$21y+16$"],"answer":[0]}},"step":1,"hints":["Cгруппируем члены выражения, содержащие $y$:$$(4y+16y)+17$$","Применим распределительное свойство умножения и выполним расчет:$$(4+16)y + 17\\newline20y+17$$"],"id":"2"},{"instruction":"Упростите выражение","content":"$29y-10-19y$[[choice-360]]","widgets":{"choice-360":{"type":"choice","options":["$10y-10$","$0$","$19y-10$"],"answer":[0]}},"step":1,"hints":["Cгруппируем члены выражения, содержащие $y$:$$(29y-19y)-10$$","Применим распределительное свойство умножения и выполним расчет:$$(29-19)y -10\\newline10y-10$$"],"id":"2"},{"instruction":"Решите уравнение","content":"$5m+25m=60$[[choice-466]]","widgets":{"choice-466":{"type":"choice","options":["$m=2$","$m=30$","$m=75$"],"answer":[0]}},"step":1,"hints":["Используя распределительное свойство умножения, преобразуем левую часть уравнения:$$(5+25)m=60 \\newline30m=60$$","Найдем неизвестный множитель:$$ m=\\frac{60}{30}\\newline m=2$$"],"id":"3"},{"instruction":"Решите уравнение","content":"$11m+39m=150$[[choice-584]]","widgets":{"choice-584":{"type":"choice","options":["$m=3$","$m=150$","$m=4$"],"answer":[0]}},"hints":["Используя распределительное свойство умножения, преобразуем левую часть уравнения:$$(11+39)m=150\\newline 50m=150$$","Найдем неизвестный множитель:$$ m=\\frac{150}{50}\\newline m=3$$"],"id":"3"},{"instruction":"Решите уравнение","content":"$66m-26m=40$[[choice-703]]","widgets":{"choice-703":{"type":"choice","options":["$m=1$","$m=2$","$m=40$"],"answer":[0]}},"step":1,"hints":["Используя распределительное свойство умножения, преобразуем левую часть уравнения:$$ (66-26)m=40\\newline40m=40$$","Найдем неизвестный множитель:$$m=\\frac{40}{40}\\newline m=1$$"],"id":"3"},{"content":"Сопоставьте выражения до и после упрощения[[matcher-833]]","widgets":{"matcher-833":{"type":"matcher","labels":["$(5x+8)\\cdot4=$","$(7x+4)\\cdot8=$","$(4x+5)\\cdot7=$"],"items":["$20x+32$","$56x+32$","$28x+35$","$35x+28$"]}},"hints":["$(\\textcolor{coral}{a}+\\textcolor{green}{b})\\cdot \\textcolor{blue}{c}=\\textcolor{coral}{a}\\textcolor{blue}{c}+\\textcolor{green}{b}\\textcolor{blue}{c}$"],"id":"4"},{"content":"Сопоставьте выражения до и после упрощения[[matcher-986]]","widgets":{"matcher-986":{"type":"matcher","labels":["$5x+5=$","$16x+32=$","$34+17x=$"],"items":["$(x+1)\\cdot5$","$(x+2)\\cdot16$","$(2+x)\\cdot17$","$(2+x)\\cdot18$"]}},"hints":["$\\textcolor{coral}{a}\\textcolor{blue}{c}+\\textcolor{green}{b}\\textcolor{blue}{c}=(\\textcolor{coral}{a}+\\textcolor{green}{b})\\cdot \\textcolor{blue}{c}$"],"id":"4"},{"content":"Сопоставьте выражения до и после упрощения[[matcher-1151]]","widgets":{"matcher-1151":{"type":"matcher","labels":["$20x-10=$","$30x-15=$","$64-24x$"],"items":["$10(2x-1)$","$15(2x-1)$","$(16-6x)\\cdot4=$","$12(3x-1)$"]}},"hints":["$\\textcolor{coral}{a}\\textcolor{blue}{c}+\\textcolor{green}{b}\\textcolor{blue}{c}=(\\textcolor{coral}{a}+\\textcolor{green}{b})\\cdot \\textcolor{blue}{c}$"],"id":"4"}]}
