{"id":244,"date":"2022-04-13T08:48:49","date_gmt":"2022-04-13T08:48:49","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=244"},"modified":"2025-04-09T11:13:32","modified_gmt":"2025-04-09T11:13:32","slug":"n-9-create-equations-with-no-solutions-or-infinitely-many-solutions","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/n-9-create-equations-with-no-solutions-or-infinitely-many-solutions\/","title":{"rendered":"N.9 Create equations with no solutions or infinitely many solutions"},"content":{"rendered":"\n

Create equations with no solutions or infinitely many solutions<\/strong><\/h2>\n\n\n\n

Key Notes :<\/p>\n\n\n\n

An equation has infinitely many solutions<\/strong> if every value of the variable makes the equation true.<\/p>\n\n\n\n

An equation has no solutions<\/strong> if no value of the variable makes the equation true.<\/p>\n\n\n\n

Learn with an example<\/strong><\/p>\n\n\n\n

\n
\n

Find the missing number so that the equation has infinitely many solutions<\/strong>.<\/p>\n\n\n\n

_____x \u2013 11 = \u2013 2x \u201311.<\/p>\n<\/div><\/div>\n\n\n\n

To find the missing number, compare both sides of the equation. If the variable terms are the same and the constant terms are the same, then the equation has infinitely many solutions.<\/p>\n\n\n\n

______x \u2013 11 = \u2013 2x \u2013 11<\/p>\n\n\n\n

The missing number is part of a variable term, so compare the constant terms first. The constant terms on both sides are \u201311.<\/p>\n\n\n\n

______x \u2013 11<\/strong> = \u2013 2x \u201311<\/strong><\/p>\n\n\n\n

So, the constant terms are the same.<\/p>\n\n\n\n

If the variable terms are also the same, then the equation has infinitely many solutions. Look at the variable terms.<\/p>\n\n\n\n

_____x \u201311=\u20132<\/strong>x\u201311<\/p>\n\n\n\n

The variable on the right is \u20132x, so the variable term on the left side should also be \u20132x. The variable terms are the same if the missing number is \u20132.<\/p>\n\n\n\n

\u20132<\/strong>x\u201311=\u20132<\/strong>x\u201311<\/p>\n\n\n\n

So, the equation has infinitely many solutions if the missing number is \u20132.<\/p>\n\n\n\n

You can check that the equation has infinitely many solutions when the missing number is \u20132. Try solving for x. Add 2x to both sides.<\/p>\n\n\n\n

\u20132x\u201311=\u20132x\u201311<\/p>\n\n\n\n

\u201311=\u201311<\/p>\n\n\n\n

This is true for any value of x. It is always true that \u201311 equals \u201311.<\/p>\n\n\n\n

So, the equation has infinitely many solutions if the missing number is \u20132.<\/p>\n<\/div><\/div>\n\n\n\n

\n
\n

Find the missing number so that the equation has infinitely many solutions<\/strong>.<\/p>\n\n\n\n

4x + ___________ = \u20134x + 14.<\/p>\n<\/div><\/div>\n\n\n\n

To find the missing number, compare both sides of the equation. If the variable terms are the same and the constant terms are the same, then the equation has infinitely many solutions.<\/p>\n\n\n\n

\u2013 4x+_____= \u20134x + 14<\/p>\n\n\n\n

The missing number is part of a constant term, so compare the variable terms first. The variable terms on both sides are \u20134x.<\/p>\n\n\n\n

\u20134<\/strong>x+______ = \u20134<\/strong>x + 14<\/p>\n\n\n\n

So, the variable terms are the same.<\/p>\n\n\n\n

If the constant terms are also the same, then the equation has infinitely many solutions. Look at the constant terms.<\/p>\n\n\n\n

\u20134x+_________= \u20134x + 14<\/strong><\/p>\n\n\n\n

The constant on the right is 14, so the constant term on the left side should also be 14. The constant terms are the same if the missing number is 14<\/strong>.<\/p>\n\n\n\n

\u20134x + 14<\/strong> = \u20134x + 14<\/strong><\/p>\n\n\n\n

So, the equation has infinitely many solutions if the missing number is 14<\/strong>.<\/p>\n\n\n\n

You can check that the equation has infinitely many solutions when the missing number is 14. Try solving for x. Add 4x to both sides.<\/p>\n\n\n\n

\u20134x + 14 = \u20134x + 14<\/p>\n\n\n\n

14 = 14<\/p>\n\n\n\n

This is true for any value of x. It is always true that 14 equals 14.So, the equation has infinitely many solutions if the missing number is 14<\/strong>.<\/p>\n<\/div><\/div>\n\n\n\n

\n
\n

Find the missing number so that the equation has no solutions<\/strong>.<\/p>\n\n\n\n

_____x + 13 = \u20132x \u2013 20<\/p>\n<\/div><\/div>\n\n\n\n

To find the missing number, compare both sides of the equation. If the variable terms are the same and the constant terms are different, then the equation has no solutions.<\/p>\n\n\n\n

______x + 13 = \u20132x \u2013 20<\/p>\n\n\n\n

The missing number is part of a variable term, so compare the constant terms first. The constant term on the left side of the equation is 13, and the constant term on the right side is \u201320.<\/p>\n\n\n\n

______x + 13<\/strong> = \u20132x \u2013 20<\/strong><\/p>\n\n\n\n

So, the constant terms are different.<\/p>\n\n\n\n

This means the equation has no solutions if the variable terms are the same. Look at the variable terms.<\/p>\n\n\n\n

______x + 13 = \u20132<\/strong>x \u2013 20<\/p>\n\n\n\n

The variable term on the right side is \u20132x, so the variable term on the left side should also be \u20132x. The variable terms are the same if the missing number is \u20132.<\/p>\n\n\n\n

\u20132<\/strong>x+13 = \u20132<\/strong>x \u201320<\/p>\n\n\n\n

So, the equation has no solutions if the missing number is \u20132.You can check that the equation has no solutions when the missing number is \u20132. Try solving for x. Add 2x to both sides.<\/p>\n\n\n\n

\u20132x+13 = \u20132x \u201320<\/p>\n\n\n\n

13 = \u201320<\/p>\n\n\n\n

No value of x makes this true. It is never true that 13 equals \u201320.So, the equation has no solutions if the missing number is \u20132.<\/p>\n<\/div><\/div>\n\n\n\n

Let’s practice!<\/p>\n\n\n\n

\n
\n
\"\"<\/a><\/figure>\n<\/div>\n\n\n\n
\n
\"\"<\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Create equations with no solutions or infinitely many solutions Key Notes : An equation has infinitely many solutions if every value of the variable makes the equation true. An equation has no solutions if no value of the variable makes the equation true. Learn with an example Find the missing number so that the equation has infinitely many solutions. _____x \u2013 11 = \u2013 2x \u201311. To find the missing number,Continue reading “N.9 Create equations with no solutions or infinitely many solutions”<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-244","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/244","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=244"}],"version-history":[{"count":20,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/244\/revisions"}],"predecessor-version":[{"id":16698,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/244\/revisions\/16698"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=244"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}