## Task 10:Solve the equation |-2x + 2| -3

Task 3:Problem 1: 5(-3x – 2) – (x – 3) = -4(4x + 5) + 13Solve the equationProblem 2:2(a -3) + 4b – 2(a -b -3) + 5Simplify the expressionProblem 3:|x – 2| – 4|-6|If x <2 simplifyProblem 4:Find the distance between the points (-4 , -5) and (-1 , -1).Problem 5:2x - 4y = 9Find the x intercept of the graph of the equation. Problem 6:Evaluate f(2) - f(1) f(x) = 6x + 1Problem 7:Find the slope of the line passing through the points (-1, -1) and (2 , 2).Problem 8:Find the slope of the line 5x - 5y = 7Problem 9:Find the equation of the line that passes through the points (-1 , -1) and (-1 , 2).Problem 10:Solve the equation |-2x + 2| -3 = -3Answers:Problem 1:Given the equation 5(-3x - 2) - (x - 3) = -4(4x + 5) + 13 Multiply factors. -15x - 10 - x + 3 = -16x - 20 +13 Group like terms.-16x - 7 = -16x - 7 Add 16x + 7 to both sides and write the equation as follows 0 = 0 Problem 2:Given the algebraic expression 2(a -3) + 4b - 2(a -b -3) + 5 Multiply factors. = 2a - 6 + 4b -2a + 2b + 6 + 5 Group like terms. = 6b + 5Problem 3:Given the expression |x - 2| - 4|-6| If x < ;2 then x - 2 < 2 and if x - 2 < 2 the |x - 2| = -(x - 2). Substitute |x - 2| by -(x - 2) and |-6| by 6 . |x - 2| - 4|-6| = -(x - 2) -4(6) = -x -22Problem 4:The distance d between points (-4 , -5) and (-1 , -1) is given byd = sqrt (-1 - -4) 2 + (-1 - -5) 2  Simplify. d = sqrt(9 + 16) = 5Problem 5:Given the equation 2x - 4y = 9 To find the x intercept we set y = 0 and solve for x. 2x - 0 = 9 Solve for x. x = 9 / 2 The x intercept is at the point (9/2 , 0).Problem 6:Given the function f(x) = 6x + 1 f(2) - f(1) is given by. f(2) - f(1) = (6*2 + 1) - (6*1 + 1) = 6Problem 7:Given the points (-1, -1) and (2 , 2), the slope m is given by m = (y2 - y1) / (x2 - x1) = (2 - -1) / (2 - -1) = 1Problem 8:Given the line5x - 5y = 7 Rewrite the equation in slope intercept form y = mx + b and identify the value of m the slope. -5y = -5x + 7 y = x - 7/5 The slope is given by the coefficient of x which is 1.Problem 9:To find the equation of the line through the points (-1 , -1) and (-1 , 2), we first use the slope m. m = (y2 - y1) / (x2 - x1) = (2 - -1) / (-1 - -1) = 3 / 0 The slope is indefined which means the line is perpendicular to the x axis and its equation has the form x = constant. Since both points have equal x coordinates -1, the equation is given by: x = -1Problem 10:The equation to solve is given by. |-2x + 2| -3 = -3 Add 3 to both sides of the equation and simplify. 1 |-2x + 2| = 0 |-2x + 2| is equal to 0 if -2x + 2 = 0. Solve for x to obtain x = 1

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