{"id":131202,"date":"2017-05-28T15:20:52","date_gmt":"2017-05-28T08:20:52","guid":{"rendered":"https:\/\/video.quipper.com\/id\/blog\/?p=131202"},"modified":"2022-02-21T23:50:30","modified_gmt":"2022-02-21T16:50:30","slug":"matematika-dasar-sbmptn-tentang-persamaan-linear-dan-pertidaksamaan-linear","status":"publish","type":"post","link":"https:\/\/quipperhome.wpcomstaging.com\/masuk-ptn\/sbmptn\/matematika-sbmptn\/matematika-dasar-sbmptn-tentang-persamaan-linear-dan-pertidaksamaan-linear\/","title":{"rendered":"Matematika Dasar SBMPTN Tentang Persamaan Linear dan Pertidaksamaan Linear"},"content":{"rendered":"<p><a href=\"http:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2017\/05\/3dfdc-blog-image-matdas-persamaan-linear.jpg\" data-rel=\"penci-gallery-image-content\" ><img fetchpriority=\"high\" decoding=\"async\" class=\"aligncenter wp-image-131212\" src=\"http:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2017\/05\/3dfdc-blog-image-matdas-persamaan-linear.jpg\" alt=\"Matematika Dasar SBMPTN Tentang Persamaan Linear dan Pertidaksamaan Linear\" width=\"800\" height=\"521\" srcset=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2017\/05\/3dfdc-blog-image-matdas-persamaan-linear.jpg 796w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2017\/05\/3dfdc-blog-image-matdas-persamaan-linear-768x500.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/a><\/p>\n<p><span style=\"font-weight: 400;\"><br \/>\n<\/span><span style=\"font-weight: 400;\">Quipperian! Pembahasan Matematika Dasar ini akan membahas tentang persamaan dan pertidaksamaan linear. Ada dua pokok bahasan, yaitu pokok bahasan I tentang persamaan linear, dan pokok bahsan II tentang pertidaksamaan linear. <\/span><\/p>\n<p><span style=\"font-weight: 400;\">Pada pokok bahasan I akan membahas mengenai penjumlahan dan perkalian, persamaan ekuvalen, persamaan pecahan, dan harga mutlak. Indikator yang diharapkan dicapai kalian setelah mempelajari kegiatan belajar mengajar 2 ini adalah kalian mampu menyelesaikan;<\/span><span style=\"font-weight: 400;\"><br \/>\n<\/span><\/p>\n<ol>\n<li><span style=\"font-weight: 400;\"> persamaan bilangan bulat satu peubah <\/span><\/li>\n<li><span style=\"font-weight: 400;\"> persamaaan pecahan satu peubah <\/span><\/li>\n<li><span style=\"font-weight: 400;\"> persamaan harga mutlak <\/span><\/li>\n<li><span style=\"font-weight: 400;\"> pertidaksamaan bilangan bulat satu peubah <\/span><\/li>\n<li><span style=\"font-weight: 400;\"> pertidaksamaan pecahan satu peubah 6. pertidaksamaan harga mutlak.<br \/>\n<\/span><\/li>\n<\/ol>\n<h2><b>Persamaan Linear<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">Suatu persamaan adalah sebuah pernyataan matematika yang terdiri dari dua ungkapan pada ruas kanan dan ruas kiri yang dipisahkan oleh tanda \u201c=\u201d (dibaca sama dengan). <\/span><\/p>\n<p><span style=\"font-weight: 400;\">Hal yang tak diketahui dalam sebuah persamaan disebut variabel, sedangkan persamaan yang memuat variabel berpangkat satu disebut persamaan linear.<br \/>\n<\/span><\/p>\n<h3 class=\"entry-title\"><a href=\"https:\/\/video.quipper.com\/id\/blog\/sbmptn\/matematika\/simak-pembahasan-soal-matematika-dasar-sbmptn\/\" target=\"_blank\" rel=\"noopener\">Simak Pembahasan Soal Matematika Dasar SBMPTN<\/a><\/h3>\n<p><span style=\"font-weight: 400;\">Contoh 2.1 <\/span><\/p>\n<ol>\n<li><span style=\"font-weight: 400;\"> x = 10 <\/span><\/li>\n<li><span style=\"font-weight: 400;\"> 4x + 1 = 15 <\/span><\/li>\n<li><span style=\"font-weight: 400;\"> 3x + 2 = x + 20<\/span><\/li>\n<\/ol>\n<p><span style=\"font-weight: 400;\">Sebuah penyelesaian dari suatu persamaan berupa bilangan yang jika disubtitusikan pada variabel menghasilkan sebuah pernyataan yang benar.<\/span><span style=\"font-weight: 400;\"><br \/>\n<\/span><span style=\"font-weight: 400;\"><br \/>\n<\/span><span style=\"font-weight: 400;\">Definisi 2.1 <\/span><\/p>\n<p><span style=\"font-weight: 400;\">Sebuah penyelesaian untuk suatu persamaan adalah sebarang bilangan yang membuat persamaan itu benar jika bilangan itu kita subtitusikan pada variabel. <\/span><\/p>\n<p><span style=\"font-weight: 400;\">Contoh 2.2 <\/span><\/p>\n<ol>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">5x = 45 persamaan ini mempunyai penyelesaian bilangan 9, sebab 5(9) = 45 adalah benar. Bilangan -8 bukan sebuah penyelesaian dari 5x = 45 sebab 5(-8) = 45 adalah salah.<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">3z + 12 = 2z + 7 jika kita selesaikan persamaan ini mempunyai penyelesaian -5 sebab 3(-5) + 12 = 2(-5) + 7<br \/>\n<\/span><\/li>\n<\/ol>\n<h2><b>Penjumlahan dan Perkalian<br \/>\n<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">Ada dua prinsip yang membolehkan kita untuk menyelesaikan bermacam-macam persamaan. Pertama, prinsip penjumlahan Untuk sebarang bilangan a, b, dan c jika a = b maka A + c = b + c A \u2013 c = b \u2013 c. <\/span><br \/>\n<span style=\"font-weight: 400;\">Kedua, prinsip perkalian Untuk sebarang bilangan real a, b, dan c jika a = b maka a . c = b . c , c b c a \u00a0benar dengan c \u2260 0 Contoh 2.3 Selesaiaklah 3x + 19 = 31 <\/span><\/p>\n<p><a href=\"http:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2017\/05\/71297-persamaan-linear.png\" data-rel=\"penci-gallery-image-content\" ><img decoding=\"async\" class=\"aligncenter wp-image-131222 size-full\" src=\"http:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2017\/05\/71297-persamaan-linear.png\" alt=\"Matematika Dasar SBMPTN Tentang Persamaan Linear dan Pertidaksamaan Linear\" width=\"543\" height=\"231\" \/><\/a><\/p>\n<h2><b>Persamaan Ekuivalen<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">Persamaan ekuivalen, adalah persamaan yang mempunyai himpunan penyelesaian yang sama. <\/span><\/p>\n<p><span style=\"font-weight: 400;\">Contoh 2.5 <\/span><\/p>\n<p><span style=\"font-weight: 400;\">4x = 16 <\/span><\/p>\n<p><span style=\"font-weight: 400;\">-5x = -20 <\/span><\/p>\n<p><span style=\"font-weight: 400;\">2x + 7 = 15 <\/span><\/p>\n<p><span style=\"font-weight: 400;\">3x \u2013 5 = x + 3 <\/span><\/p>\n<p><span style=\"font-weight: 400;\">Keempat persamaan tersebut ekivalen karena himpunan penyelesaiannya sama, yaitu x x 4.<\/span><\/p>\n<p>&nbsp;<\/p>\n<h2><b>Persamaan Pecahan<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">Persamaan yang memuat ungkapan pecahan kita namakan persamaan pecahan. Untuk menyelesaikan persamaan pecahan ini kita gunakan perkalian dengan variabel. <\/span><\/p>\n<h2><b>Pertidaksamaan Linear <\/b><\/h2>\n<p><span style=\"font-weight: 400;\">Suatu kalimat matematika yang mengandung satu atau lebih peubah dan relasi \u2264, \u02c2, \u2265 atau \u02c3 disebut suatu pertidaksamaan. Perhatikan contoh-contoh berikut. <\/span><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-weight: 400;\">1). x + 7 \u02c3 4 <\/span><\/p>\n<p><span style=\"font-weight: 400;\">2). x \u2013 4 \u2264 7 + 3x <\/span><\/p>\n<p><span style=\"font-weight: 400;\">3). x + y &lt; 3 5). x2 + y2 &lt; 0 <\/span><\/p>\n<p><span style=\"font-weight: 400;\">4). x 2 \u2013 4x +2 \u2265 0 <\/span><\/p>\n<h3 class=\"entry-title\"><a href=\"https:\/\/video.quipper.com\/id\/blog\/sbmptn\/matematika\/catat-contoh-materi-yang-keluar-di-soal-matematika-dasar-sbmptn\/\" target=\"_blank\" rel=\"noopener\">Catat! Contoh Materi yang Keluar di Soal Matematika Dasar SBMPTN<\/a><\/h3>\n<p><span style=\"font-weight: 400;\">Jika suatu pertidaksamaan hanya mengandung satu peubah dan berpangkat satu maka pertidaksamaan tersebut dinamakan pertidaksamaan linear satu peubah. Selanjutnya jika dikatakan pertidaksamaan, maka yang dimaksud adalah pertidaksamaan linear satu peubah. Contoh 1 dan 2 merupakan suatu pertidaksamaan linear satu peubah, sedang contoh 3, 4, dan 5 bukan.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Bentuk umum pertidaksaman linear satu peubah adalah ax + b \u2264 0, ax + b &lt; 0, ax + b \u2265 0, dan ax +b &gt; 0 dengan a, b bilangan real dan a \u2260 0. Sebagaimana halnya persamaan, menyelesaikan pertidaksamaan merupakan suatu proses mendapatkan suatu bilangan sehingga pertidaksamaan tersebut menjadi proposisi benar. <\/span><\/p>\n<p><span style=\"font-weight: 400;\">Bilangan yang diperoleh tersebut merupakan selesaian pertidaksamaan tersebut. Himpunan semua selesaian suatu pertidaksamaan disebut himpunan selesaian.<br \/>\n<\/span><\/p>\n<h2><b>RANGKUMAN<\/b><\/h2>\n<p><b>Persamaan dan pertidaksamaan linear <\/b><\/p>\n<p><span style=\"font-weight: 400;\">Jika semesta pembicaraan tidak dinyatakan secara khusus, maka semesta pembicaraan adalah himpunan bilangan real. <\/span><\/p>\n<ol>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Peramaan linear Suatu kalimat matematika yang mengandung satu atau lebih peubah dan relasi \u201c=\u201d disebut persamaan. Suatu persamaan yang mengandung satu peubah dan berpangkat satu disebut persamaan linear satu peubah. <\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Pertidaksamaan linear 27 Suatu kalimat matematika yang mengandung satu atau lebih peubah dan relasi \u201c,,, atau \u00a0\u201d disebut suatu pertidaksamaan. Suatu pertidaksamaan yang mengandung satu peubah dan berpangkat satu, maka pertidaksamaan itu disebut pertidaksamaan linear satu peubah.<\/span><\/li>\n<\/ol>\n<p><b>Penulis: Sritopia<\/b><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Quipperian! Pembahasan Matematika Dasar ini akan membahas tentang persamaan dan pertidaksamaan linear. Ada dua pokok bahasan, yaitu pokok bahasan I tentang persamaan linear, dan&hellip;<\/p>\n","protected":false},"author":156446345,"featured_media":131212,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_monsterinsights_skip_tracking":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_wpcom_ai_launchpad_first_post":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[253044991],"tags":[169291195],"ppma_author":[679386822],"class_list":["post-131202","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-matematika-sbmptn","tag-contoh-soal-sbmptn"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.2 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Matematika Dasar SBMPTN Tentang Persamaan Linear dan Pertidaksamaan Linear<\/title>\n<meta name=\"description\" content=\"Quipperian, materi persamaan linear dan pertidaksamaan linear ini terkadang suka menjebak saat ujian. 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