{"appState":{"pageLoadApiCallsStatus":true},"articleState":{"article":{"headers":{"creationTime":"2017-04-26T00:45:54+00:00","modifiedTime":"2017-04-26T00:45:54+00:00","timestamp":"2022-09-14T18:18:35+00:00"},"data":{"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Study Skills & Test Prep","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33772"},"slug":"study-skills-test-prep","categoryId":33772},{"name":"ACT","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33775"},"slug":"act","categoryId":33775}],"title":"ACT Practice Math Questions: Inequalities","strippedTitle":"act practice math questions: inequalities","slug":"act-practice-math-questions-inequalities","canonicalUrl":"","seo":{"metaDescription":"All things being equal, the chances that you'll have to solve some inequalities on the ACT Math exam are very good. Fortunately, the following practice question","noIndex":0,"noFollow":0},"content":"All things being equal, the chances that you'll have to solve some inequalities on the ACT Math exam are very good. Fortunately, the following practice questions will help you become greater than the challenge!\r\n<h2 id=\"tab1\" >Practice questions</h2>\r\n<ol>\r\n\t<li>Given that <em>x</em> is an integer, for what value of <em>x</em> is\r\n\r\n<a href=\"https://www.dummies.com/wp-content/uploads/ACT_1801.gif\"><img class=\"alignnone size-full wp-image-238630\" src=\"https://www.dummies.com/wp-content/uploads/ACT_1801.gif\" alt=\"ACT_1801\" width=\"84\" height=\"45\" /></a>\r\n\r\nand <em>x</em> + 4 < 16?\r\n\r\n<strong>A.</strong> 7\r\n<strong>B.</strong> 8\r\n<strong>C.</strong> 10\r\n<strong>D.</strong> 12\r\n<strong>E.</strong> 13</li>\r\n\t<li>Which of the following represents all possible solutions for <em>x</em> in the inequality –2<em>x</em> – 7 < 3<em>x</em> + 5?\r\n\r\n<a href=\"https://www.dummies.com/wp-content/uploads/ACT_1802.gif\"><img class=\"alignnone size-medium wp-image-238631\" src=\"https://www.dummies.com/wp-content/uploads/ACT_1802-82x255.gif\" alt=\"ACT_1802\" width=\"82\" height=\"255\" /></a></li>\r\n</ol>\r\n<h2 id=\"tab2\" >Answers and explanations</h2>\r\n<ol>\r\n\t<li>The correct answer is Choice <strong>(C).\r\n\r\n</strong>Instead of working out complex calculations, first examine the answer choices. Based on the second equation, you can eliminate Choices (D) and (E). Neither 13 + 4 nor 12 + 4 is less than 16.\r\n\r\nThen plug the remaining options into the first equation. Because you're determining which answer results in a value greater than 16, start with the greatest value, 10.\r\n\r\nIf <em>x</em> is 10 in the first expression, then\r\n\r\n<a href=\"https://www.dummies.com/wp-content/uploads/ACT_1803.gif\"><img class=\"alignnone size-full wp-image-238632\" src=\"https://www.dummies.com/wp-content/uploads/ACT_1803.gif\" alt=\"ACT_1803\" width=\"167\" height=\"45\" /></a>\r\n\r\nwhich is certainly more than 16. The first equation is valid.\r\n\r\nTry the second: 10 + 4 < 16. This inequality is also true, so the answer must be Choice (C).\r\n\r\nYou can try the other options, but neither <em>x</em> = 7 nor <em>x</em> = 8 results in a value greater than 16.</li>\r\n\t<li>The correct answer is Choice <strong>(B).\r\n\r\n</strong>Solve the inequality just as you would an ordinary equation. Move all the constants to the right and all the <em>x</em> terms to the left:\r\n\r\n<a href=\"https://www.dummies.com/wp-content/uploads/ACT_1804.gif\"><img class=\"alignnone size-full wp-image-238633\" src=\"https://www.dummies.com/wp-content/uploads/ACT_1804.gif\" alt=\"ACT_1804\" width=\"119\" height=\"123\" /></a>\r\n\r\nChoice (B) is the answer.\r\n\r\nChoice (A) is wrong because you must change the direction of the sign when you divide both sides of an inequality by a negative value.</li>\r\n</ol>","description":"All things being equal, the chances that you'll have to solve some inequalities on the ACT Math exam are very good. Fortunately, the following practice questions will help you become greater than the challenge!\r\n<h2 id=\"tab1\" >Practice questions</h2>\r\n<ol>\r\n\t<li>Given that <em>x</em> is an integer, for what value of <em>x</em> is\r\n\r\n<a href=\"https://www.dummies.com/wp-content/uploads/ACT_1801.gif\"><img class=\"alignnone size-full wp-image-238630\" src=\"https://www.dummies.com/wp-content/uploads/ACT_1801.gif\" alt=\"ACT_1801\" width=\"84\" height=\"45\" /></a>\r\n\r\nand <em>x</em> + 4 < 16?\r\n\r\n<strong>A.</strong> 7\r\n<strong>B.</strong> 8\r\n<strong>C.</strong> 10\r\n<strong>D.</strong> 12\r\n<strong>E.</strong> 13</li>\r\n\t<li>Which of the following represents all possible solutions for <em>x</em> in the inequality –2<em>x</em> – 7 < 3<em>x</em> + 5?\r\n\r\n<a href=\"https://www.dummies.com/wp-content/uploads/ACT_1802.gif\"><img class=\"alignnone size-medium wp-image-238631\" src=\"https://www.dummies.com/wp-content/uploads/ACT_1802-82x255.gif\" alt=\"ACT_1802\" width=\"82\" height=\"255\" /></a></li>\r\n</ol>\r\n<h2 id=\"tab2\" >Answers and explanations</h2>\r\n<ol>\r\n\t<li>The correct answer is Choice <strong>(C).\r\n\r\n</strong>Instead of working out complex calculations, first examine the answer choices. Based on the second equation, you can eliminate Choices (D) and (E). Neither 13 + 4 nor 12 + 4 is less than 16.\r\n\r\nThen plug the remaining options into the first equation. Because you're determining which answer results in a value greater than 16, start with the greatest value, 10.\r\n\r\nIf <em>x</em> is 10 in the first expression, then\r\n\r\n<a href=\"https://www.dummies.com/wp-content/uploads/ACT_1803.gif\"><img class=\"alignnone size-full wp-image-238632\" src=\"https://www.dummies.com/wp-content/uploads/ACT_1803.gif\" alt=\"ACT_1803\" width=\"167\" height=\"45\" /></a>\r\n\r\nwhich is certainly more than 16. The first equation is valid.\r\n\r\nTry the second: 10 + 4 < 16. This inequality is also true, so the answer must be Choice (C).\r\n\r\nYou can try the other options, but neither <em>x</em> = 7 nor <em>x</em> = 8 results in a value greater than 16.</li>\r\n\t<li>The correct answer is Choice <strong>(B).\r\n\r\n</strong>Solve the inequality just as you would an ordinary equation. Move all the constants to the right and all the <em>x</em> terms to the left:\r\n\r\n<a href=\"https://www.dummies.com/wp-content/uploads/ACT_1804.gif\"><img class=\"alignnone size-full wp-image-238633\" src=\"https://www.dummies.com/wp-content/uploads/ACT_1804.gif\" alt=\"ACT_1804\" width=\"119\" height=\"123\" /></a>\r\n\r\nChoice (B) is the answer.\r\n\r\nChoice (A) is wrong because you must change the direction of the sign when you divide both sides of an inequality by a negative value.</li>\r\n</ol>","blurb":"","authors":[{"authorId":9086,"name":"Lisa Zimmer Hatch","slug":"lisa-zimmer-hatch","description":" <p><b>Lisa Zimmer Hatch </b>served as VP of The Center for Legal Studies, where she created standardized test preparation. Currently, she is an Independent College Counselor and president of College Primers.</p> <p><b>Scott A. Hatch</b> develops courses for a variety of careers and assists those seeking advanced degrees in law, business, and other professions. ","hasArticle":false,"_links":{"self":"https://dummies-api.dummies.com/v2/authors/9086"}},{"authorId":9087,"name":"Scott A. Hatch","slug":"scott-a-hatch","description":" <p><b>Lisa Zimmer Hatch </b>served as VP of The Center for Legal Studies, where she created standardized test preparation. Currently, she is an Independent College Counselor and president of College Primers.</p> <p><b>Scott A. Hatch</b> develops courses for a variety of careers and assists those seeking advanced degrees in law, business, and other professions. 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ACT Practice Math Questions: Inequalities

By: Lisa Zimmer Hatch and Scott A. Hatch and

Updated: 04-26-2017

From The Book: ACT

ACT

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All things being equal, the chances that you'll have to solve some inequalities on the ACT Math exam are very good. Fortunately, the following practice questions will help you become greater than the challenge!

Practice questions

Given that x is an integer, for what value of x is
and x + 4 < 16?
A. 7 B. 8 C. 10 D. 12 E. 13
Which of the following represents all possible solutions for x in the inequality –2x – 7 < 3x + 5?

Answers and explanations

The correct answer is Choice (C).
Instead of working out complex calculations, first examine the answer choices. Based on the second equation, you can eliminate Choices (D) and (E). Neither 13 + 4 nor 12 + 4 is less than 16.
Then plug the remaining options into the first equation. Because you're determining which answer results in a value greater than 16, start with the greatest value, 10.
If x is 10 in the first expression, then
which is certainly more than 16. The first equation is valid.
Try the second: 10 + 4 < 16. This inequality is also true, so the answer must be Choice (C).
You can try the other options, but neither x = 7 nor x = 8 results in a value greater than 16.
The correct answer is Choice (B).
Solve the inequality just as you would an ordinary equation. Move all the constants to the right and all the x terms to the left:
Choice (B) is the answer.
Choice (A) is wrong because you must change the direction of the sign when you divide both sides of an inequality by a negative value.

About This Article

This article is from the book:

ACT ,

About the book authors:

Lisa Zimmer Hatch, MA, and Scott A. Hatch, JD, have been helping students excel on standardized tests and navigate the college admissions process since 1987. They have written curricula and taught students internationally through live lectures, online forums, DVDs, and independent study.

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