If $k$ is an integer and $-3 < 2k + 1 \\le 5$, the possible values are {{blank:a}}, {{blank:b}}, {{blank:c}} and {{blank:d}}."},{"id":"card-16","type":"multi-question","order":16,"questions":[{"id":"mq-1","options":[{"id":"a","text":"$$x$ is less than 7 only","isCorrect":false},{"id":"b","text":"$$x$ is greater than or equal to 7","isCorrect":false},{"id":"c","text":"$$x$ is less than or equal to 7","isCorrect":true}],"question":"What does $x \\le 7$ mean?","explanation":"The symbol $\\le$ represents 'less than or equal to'."},{"id":"mq-2","options":[{"id":"a","text":"An open circle","isCorrect":true},{"id":"b","text":"A solid circle","isCorrect":false},{"id":"c","text":"No endpoint mark","isCorrect":false}],"question":"For $x > 5$, what should be drawn at 5 on a number line?","explanation":"Strict inequalities ($>$ or $<$) use an open circle because the value itself is not included."},{"id":"mq-3","options":[{"id":"a","text":"$$p < 4$","isCorrect":true},{"id":"b","text":"$$p > 4$","isCorrect":false},{"id":"c","text":"$$p < 7$","isCorrect":false}],"question":"Solve $2p + 3 < 11$.","explanation":"Subtract 3: $2p < 8$. Divide by 2: $p < 4$."},{"id":"mq-4","options":[{"id":"a","text":"$$x \\ge 4$","isCorrect":false},{"id":"b","text":"$$x \\le 4$","isCorrect":true},{"id":"c","text":"$$x < 4$","isCorrect":false}],"question":"Solve $6 - x \\ge 2$.","explanation":"Subtract 6: $-x \\ge -4$. Divide by $-1$ and flip the inequality sign: $x \\le 4$."},{"id":"mq-5","options":[{"id":"a","text":"$$r > 5$","isCorrect":false},{"id":"b","text":"$$r > 3$","isCorrect":true},{"id":"c","text":"$$r < 3$","isCorrect":false}],"question":"Solve $2(r + 1) > 8$.","explanation":"Divide by 2: $r + 1 > 4$. Subtract 1: $r > 3$."},{"id":"mq-6","options":[{"id":"a","text":"$$a \\le 4$","isCorrect":true},{"id":"b","text":"$$a \\ge 4$","isCorrect":false},{"id":"c","text":"$$a \\le 8$","isCorrect":false}],"question":"Solve $3a + 2 \\le a + 10$.","explanation":"Subtract $a$ from both sides: $2a + 2 \\le 10$. Subtract 2: $2a \\le 8$. Divide by 2: $a \\le 4$."},{"id":"mq-7","options":[{"id":"a","text":"2","isCorrect":false},{"id":"b","text":"3","isCorrect":true},{"id":"c","text":"4","isCorrect":false}],"question":"If $q$ is an integer and $1 \\le q < 4$, how many possible values are there?","explanation":"The possible integer values are 1, 2, and 3. 4 is excluded because the sign is strictly less than."}]}],"isPublished":true,"createdAt":"2026-05-13T10:37:00.581Z","updatedAt":"2026-05-13T10:48:18.602Z"},"lessonHref":"/gcse/maths/edexcel/grade-4-4-5-inequalities/lessons","lessonTitle":"Inequalities","subjectId":"e8dff79f-b531-4d5f-9de3-09e10125a637","subjectName":"Maths","subjectSlug":"maths","topicSidebar":"$L3c","previewCardCount":4,"topicSlug":"grade-4-4-5-inequalities","topicUrl":"/gcse/maths/edexcel/grade-4-4-5-inequalities"}],"$L3d"]}]

Inequalities Lesson

Inequalities Lesson