Algebra 2 Part 5 Chapter1

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"Literal Equations' is the next section. "'Literal equations, or formulas, can be rearranged to solve for a variable. Example 1.7 Solve P = 2w + 2l for w Solution P = 2w + 2l Common Error P - 2crossed off times l/2 crossed off = w P -2l = 2w P - l = w "The 2s cannot be canceled in this P - 2l/2 = w fraction. See Chapter 9." "In addition to using the addition and multiplication properties of equality, you may also need to factor a 'greatest common factor' to solve some literal equations." Example 1.8 Solve ax + c = bx + 10 for x Solution ax + c = bx +10 Move all terms with x to one side. Move all terms ax - bx = 10 -c without x to the other side. x(a - b) = 10 - c Factor x out of each term on the left side. x(a - b)/a -b = 10 - c/a - b Divide each side by a - b to get x by itself. x = 10 - c/a - b Note that the solution assumes a is not equal b. If a = b, the equation has no solution (unless c = 10, in which case the original equation is an identity)." Section Exercises Solve each Equation for x. Answers 1-1. 7(x - 3) - 5(2x - 4 = 5 x = -2 1-2. x/x +6 = x - 2/x x = 3 1-3. 3(x + 2) - 11 = 5(x - 4) x = 7. 1-4. a/x = 3/x - a x = a to the exponent of 2/a - 3 1-5. Solve S = 2pie rh + pie r to the exponent 2 for h. h = S - pie r to the exponent of 2/2 pie r 1-6. ax + b = c(x + 1) x = c - b/a - c