1.6+Solve+linear+inequalities

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 * 1.6 Solve Linear Inequalities **

** Key Vocabulary ** Linear Inequality: is a variable that can be written in one of the following forms, where __a__ and __b__ are real numbers and __a__ is not equal to 0. ax+b<0 ax+b>0 ax+b__<__0 ax+b__>__0  Compound Inequality: consists of two simple inequalities joined by "and" or "or". Equivalent Inequalities: inequalities that have the same solutions as the original inequality. ** KEY CONCEPT **
 * Transformation  applied to inequality  ||  Original   inequality  ||  Equivalent   inequality  ||
 * ** Add ** the same number to each side. || //x// - 7 < 4 || //x// < 11 ||
 * ** Subtract ** the same number from each side. || //x// + 3 __>__ -1 || //x// __>__ -4 ||
 * ** Multiply ** each side by the same //positive// number. || 1/2//x// > 10 || //x// > 20 ||
 * ** Divide ** each side by the same //positive// number. || 5//x// __<__ 15 || //x// __<__ 3 ||
 * ** Multiply ** each side by the same //negative// number and //reverse// the inequality. || -//x// < 17 || //x// > -17 ||
 * **Divide** each side by the same //negative// number and //reverse// the inequality. || -9 > 45 || //x// < -5 ||

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1.) Graph the compound inequality.  2 __<__ x __<__ 5
 * Assessment **

3.) Solve the inequality. If there is no solution, write //no solution//. If

the inequality is

always true, write //all real// //numbers//.

2(x - 4) > 2x + 1

** Answers **

2.) b.)x < -1 or x > 3 No Solution
 * 3.) ||  2(x - 4)>  ||<  2x + 1  ||
 * || 2x - 8 >  ||  2x + 1  ||
 * || -2x  ||  -2x  ||
 * || -8 > 1  ||   ||