Simplifying Expressions Essay Example for Free

Simplifying Expressions Essay Include in this paper I have demonstrated the following solutions for the three problems listed below. Using th given vocabulary words I have broken down each problem using the proper steps in solving the algebraic expressions. Also shown will be what is important about real numbers and in what way they are useful in using real numbers in solving algebraic expressions. By breaking down the equation you can simplify the equation down to lowest terms. Gathering the like terms in the equation is a step in breaking down the expression correctly. Take the coefficient and multiply it by the variable. The distributive property in the expression is the letters in the expression. When solving a algebraic expression you always remove the parenthesis first. A. )2a(-5 + a) + 4(a + -5) Simplify the terms (-5 * 2a + a * 2a) + 4(a + -5) (-10a + 2a2) + 4(a + -5) -10a + 2a2 + 4(-5 + a)Reorder the terms -10a + 2a2 + (-5 * 4 + a * 4) -10a + 2a2 + (-20 + 4a) -10a + 4a = -6a -20 + -6a + 2a2 Combine the like terms : -20 + -6a + 2a2 a = 5This is the simplified answer  a = {-2, 5} B. ) 2w – 3 + 3(w – 4) – 5(w – 6)The given expression -3 + -12 + 30 + 2w + 3w + -5w The distributive property removes the parentheses. -15 + 30 + 2w + 3w + -5w Combine the like terms 15 + 2w + 3w + -5w = 0Combine the like terms 2w + 3w = 5wCombine like terms again 15 + 5w + -5w 5w + -5w 15 + 0 15 = 0The final answer C. ) 0. 05(0. 3m + 35n) + -0. 8(-0. 09n + -22m) (0. 3m * 0. 05 + 35n * 0. 05) + -0. 8(-0. 09n + -22m) (0. 015m + 1. 75n) + -0. 8(-0. 09n + -22m) 0. 015m + 1. 75n + -0. 8(-22m + -0.09n) Reorder the terms 0. 015m + 1. 75n + (-22m * -0. 8 + -0. 09n * -0. 8) 0. 015m + 1. 75n + (17. 6m + 0. 072n) 0. 015m + 17. 60. 1034345728n m + 1. 75n + 0. 072n The distributive property removes the parentheses 0. 015m + 17. 6m = 17. 615mCombine the like terms 17. 615m + 1. 75n + 0. 072n 1. 75n + 0. 072n = 1. 822nCombine the like terms 17. 615m + 1. 822n 17. 615m + 1. 822n Solving Move all terms containing m to the left, all other terms to the right. Add -1. 822n to each side of the equation. 17.615m + 1. 822n + -1. 822n = 0 + -1. 822n Combine like terms: 1. 822n + -1. 822n = 0. 000 17. 615m + 0. 000 = 0 + -1. 822n 17. 615m = 0 + -1. 822n Remove the zero: 17. 615m = -1. 822n Divide each side by 17. 615. m = -0. 1034345728n Simplifying m = -0. 1034345728n How are the real numbers useful in solving algebraic expressions? The real number line is a graph that is used to represent the set of real numbers. Using real numbers is useful by charting them on the graph helps to solve the algebraic expression.