If 8x -3 <0 and 8x>0, express these in a continued inequality and find its solution.<\/p>\n\n\n\n
The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n We have two inequalities:<\/p>\n\n\n\n We need to combine<\/strong> them into a compound (continued) inequality<\/strong> and then solve<\/strong> it.<\/p>\n\n\n\n 8x\u22123<08x – 3 < 0<\/p>\n\n\n\n Add 3 to both sides: 8x<38x < 3<\/p>\n\n\n\n Divide both sides by 8: x<38x < \\frac{3}{8}<\/p>\n\n\n\n 8x>08x > 0<\/p>\n\n\n\n Divide both sides by 8: x>0x > 0<\/p>\n\n\n\n From above: 0<x<380 < x < \\frac{3}{8}<\/p>\n\n\n\n 0<x<38\\boxed{0 < x < \\frac{3}{8}}<\/p>\n\n\n\n In this problem, we are given two separate inequalities: 8x\u22123<08x – 3 < 0 and 8x>08x > 0. The goal is to combine them into a single continued inequality and find the range of values for xx that satisfy both conditions simultaneously<\/strong>.<\/p>\n\n\n\n Let\u2019s first solve each inequality one at a time. Starting with 8x\u22123<08x – 3 < 0, we isolate xx by first adding 3 to both sides, giving 8x<38x < 3, and then divide by 8 to get x<38x < \\frac{3}{8}. This means that xx must be less than 38\\frac{3}{8}.<\/p>\n\n\n\n Now, let\u2019s solve the second inequality 8x>08x > 0. Divide both sides by 8 to get x>0x > 0. This tells us that xx must also be greater than 0.<\/p>\n\n\n\n To find the values of xx that satisfy both<\/strong> inequalities, we look for the overlap or intersection between the two solutions. x<38x < \\frac{3}{8} overlaps with x>0x > 0 in the range where: 0<x<380 < x < \\frac{3}{8}<\/p>\n\n\n\n This is called a compound inequality<\/strong>, which shows a range of numbers that satisfy two or more conditions. Visually, on a number line, this would be an open interval between 0 and 38\\frac{3}{8}, excluding both endpoints.<\/p>\n\n\n\n In conclusion, the solution to the combined inequality is: 0<x<38\\boxed{0 < x < \\frac{3}{8}}<\/p>\n\n\n\n This means xx can be any real number<\/strong> between 0 and 38\\frac{3}{8}, but not equal<\/strong> to either endpoint.<\/p>\n","protected":false},"excerpt":{"rendered":" If 8x -3 <0 and 8x>0, express these in a continued inequality and find its solution. The correct answer and explanation is: Given: We have two inequalities: We need to combine them into a compound (continued) inequality and then solve it. Step 1: Solve each inequality individually. Inequality 1: 8x\u22123<08x – 3 < 0 Add […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-15983","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/15983","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=15983"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/15983\/revisions"}],"predecessor-version":[{"id":15984,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/15983\/revisions\/15984"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=15983"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=15983"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=15983"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Given:<\/h3>\n\n\n\n
\n
\n\n\n\nStep 1: Solve each inequality individually.<\/h3>\n\n\n\n
Inequality 1:<\/h4>\n\n\n\n
\n\n\n\nInequality 2:<\/h4>\n\n\n\n
\n\n\n\nStep 2: Combine into a continued inequality.<\/h3>\n\n\n\n
\n\n\n\n\u2705 Final Answer:<\/h3>\n\n\n\n
\n\n\n\n\ud83d\udcd8 Explanation (Approx. 300 words):<\/h3>\n\n\n\n