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Literal Equations & Inequalities Literal: More than one variable To solve for a variable means to rewrite an equation as an equivalent equation in which the variable is on one side and does not appear on the other side. Example: Area of a triangle 1 Solve A bh for the height. Find the height of a triangle with a base of 4 in and area of 18 in2. 2 2(18) h 2A bh 4 2A h 9 in h b 1 Example: Area of a trapezoid - Solve A (b1 b2 )h for b1 . 2 2 A (b1 b2 )h 2A b1 b2 h 2A b1 b2 h Example: Solve bx + ux + ch = er for x x(b u ) ch er *make sure to factor out the x so that there is only one! x(b u ) er ch er ch x bu Example: Solve x hx a for x m m x hx m ma m m m x ma h x 2x ma h ma h x 2 3( x 1) x 4 5 3 Lowest common denominator is 15 Example: Solve 2 x 3( x 1) x 15 2 x 4 5 3 30 x 9( x 1) 5 x 60 30x 9x 9 5x 60 34x 69 69 x 34 Linear Inequality – can be written in one of the following forms, where a and b are real numbers and a 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”. Solution – a value that, when substituted for the variable, results in a true statement. Graph – all points on a number line that represent solutions. Solution Set – a range of answers is written in brackets with the lower bound listed first, then a comma, then the upper bound. We use soft brackets ( ) when the bounds are non-inclusive (< and >). We use hard brackets [ ] when the bounds are included ( and ) Example: 4 2x ; {reals} 2 x 2 x 1 **Remember to switch the sign when dividing by a negative! Graph on a number line: Solution in interval notation: (, 1) Example: **always write your solution set from least to greatest **always use () for 8(2 x 1) 11x 17 ; {integers} 16x 8 11x 17 16x 11x 9 5x 9 9 x 5 Graph: *Since the domain is {integers}, only graph dots on the integers Solution: { -1, 0, 1, … } **list specific integers in the solution set Example: 5 2x 3 15 ; {reals} 8 2 x 12 4 x 6 Compound inequality. Break it up. Graph: Solution: (-4, 6) Example: x 7 4 or 7 x 1 ; {reals} x 3 x6 Graph: Solution: , 3 6, sometimes written , 3 This is called a “disjunction” 6,