# Algebra Tutorial

This is a tutorial with detailed solutions and matched exercises on algebra: solve linear equations and equations with absolute value, simplify expressions, find the intercepts of a graph, find the slope of a line and equations of lines. Detailed solutions and explanations ( in red) are provided.

 A self test on algebra problems related to topics similar to those in this tutorial can be found in this website. Example 1: Simplify the expression 2(-4a - 5b) - (8 + b) + b + (-2b + 4) - 5a Solution to Example1 given 2(-4a - 5b) - (8 + b) + b + (-2b + 4) - 5a multiply factors -8a - 10b - 8 - b + b -2b + 4 - 5a group like terms - 13a - 12b - 4 Matched Exercise 1 Simplify the expression 2(a - 8b) - (5 - b) + b + (6b - 9) - a Example 2: Solve the equation 2(-3x - 5) - (8 - x) = -2(2x + 4) + 12 Solution to Example 2 given 2(-3x - 5) - (8 - x) = -2(2x + 4) + 12 multiply factors -6x -10 - 8 + x = -4x - 8 + 12 group like terms -5x - 18 = -4x + 4 add 18 to both sides -5x -18 + 18 = -4x + 4 + 18 group like terms -5x = -4x + 22 add 4x to both sides -5x + 4x = -4x + 22 +4x group like terms -x = 22 multiply both sides by -1 x = -22 Check the solution left side:2(-3*(-22) - 5) - (8 - (-22)) = 92 right side:-2(2(-22) +4) + 12 = 92 Conclusion x = -22 is the solution to the given equation Matched Exercise 2: Solve the equation 2(-x - 5) - (-6 + x) = -3(2x + 4) + 12 /* script-replace-4c7a41ebe650b2c20ebe2a8e80d88f02 */ Example 3: If x > -2, simplify the expression 2| x + 2 | - 3x - (-2 - x) + | 6 - 9 | Solution to Example 3 To simplify the given expression, we need to simplify the terms with absolute value using definition of absolute value. if x > = 0 , | x | = x if x < 0 , | x | = -x According to the definition of the absolute value above, x > - 2 (given above) is equivalent to x + 2 > 0 if x + 2 > 0 then | x + 2 | = x + 2 the above definition gives | 6 - 9 | = | - 3 | = 3 the whole expression given above can now be written as 2(x + 2) - 3x - (-2 - x) + 3 multiply factor 2x + 4 -3x + 2 + x + 3 group like terms 9 Matched Exercise 3: If x > 3, simplify the expression 2| x - 3 | + 6x - (2 - 3x) + | 9 - 20 | Example 4: Find the slope and the y-intercept of the line given by the equation 2y - 3x = 10 Solution to Example 4 We first write the equation in slope intercept form y = mx +b. Put terms in x and constant terms on the right side 2y = 3x + 10 Divide both sides by 2 y = (3/2)x + 5 Now that the equation is in slope intercept form, we identify the slope as the coefficient of x and is equal to 3/2 and the y intercept as (0 , 5). Matched Exercise 4: Find the slope and the y-intercept of the line given by the equation -3y - 6x = 7 Example 5: Find the equation of the line passing through the points (2 , 3) and (4 , 1).Solution to Example 5 We first calculate the slope m m = (1 - 3) / (4 - 2) = -1 We now use the point-slope form of a line to find the equation of the line y - y1 = m(x - x1) , where m is the slope and (x1,y1) is any of the two points given above. Substitute m by its value -1 and x1 and y1 by 2 and 3 respectively, we obtain the equation of the line. y - 3 = -1(x - 2) in slope intercept form the equation is written as y = -x + 5 Matched Exercise 5: Find the equation of the line passing through the points (0 , 3) and (-1 , 1). More links and references to pages with algebra problems, tutorials and self tests.

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