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Reasoning & Algebraic Proof
Solve Equations & Inequalities
Graphing Equations & Inequalities in 2 variables
Solve Systems by Elimination & Substitution
Solve Systems by Graphing
100
The steps and properties used in the equation: 4x - 3x + 2 = 6
What is: 4x - 3x + 2 = 6 Given Equation x + 2 = 6 Substitution Property of Equality x = 4 Subtraction Property of Equality
100
The solution to 10x + 3 > 2x - 21.
What is x>-3
100
The Graph of 7x - y = -3
What is ... See student diagram... The graph of the line in slope intercept form is y = 7x + 3 Where the line intercepts the y-axis at + 3 and has a positive slope with a rise of 7 and a run of 1...
100
The solution to the sytem of equations using substitution 4x + 2y = 10 & x - y = 13
What is (6, -7)
100
The solution to the system of equations by graphing: y = - 3x + 4 & y = 3x - 2
What is (1, 1)
200
The steps and properties used in the equation: 5(2 - 4x) + 8 = 28
What is: 5(2 - 4x) + 8 = 28 Given Equation 10 - 20x + 8 = 28 Distributive Property 18 - 20x = 28 Substitution Property of Equality -20x = 10 Subtraction Property of Equality x = -10/20 Division Property of Equality x = - 1/2 Substitution (or simplifcation)
200
2x/3 + 4 < 2x + 12
What is x > -6
200
The Graphical Solution to the following inequality: 4x +y < 2
What is ... See student diagram... The inequality in slope intercept from is y < -4x + 2. The graph of the "Boundary line" y = -4x + 2 intercepts the y-axis at + 2... The graph of the boundary line has a negative slope with a rise of - 4 (falls 4 units) and a run of + 1... The boundary line is DOTTED (since y can NOT = -4x + 2) The portion BELOW (and to the left of) the boundary line is SHADED
200
The solution to the sytem of equations using elimination -8x - 10y = 24 & 6x + 5y = 2
What is (7, -8)
200
The solution to the system of equations by graphing: y = x + 2 & x = - 3
What is (-3, -1)
300
The steps and properties used in the equation: 4x - 3(2 - 6x) = -50
What is: 4x - 3(2 - 6x) = -50 Given Equation 4x - 6 + 18x = -50 Distributive Property 4x +18x = -44 Addition Property of Equality 22x = -44 Substitution Property of Equality x = -2 Division Property of Equality
300
The solution to: 3^x - 20 = 61
What is x = 4
300
The Graphical Solution to the following system of inequalities: 3x + 2y > -2 & x - 2y ≤ -4
See student diagram... The first inequality in slope intercept form is y > -3x/2 - 1 The graph of the "Boundary line" y = -3x/2 - 1 intercepts the y-axis at - 1. The boundary line has a negative slope with a rise of - 3 (falls 3 units) and a run of + 2... The boundary line is DOTTED (since y can NOT = -3x/2 - 1) The portion ABOVE (and to the right of) the boundary line is SHADED The second inequality in slope intercept form is y ≥ 1x/2 +2 The graph of the "Boundary line" y = 1x/2 +2 intercepts the y-axis at + 2. The boundary line has a poitive slope with a rise of 1 and a run of + 2... The boundary line is SOLID (since y can also = 1x/2 +2) The portion ABOVE (and to the left of) the boundary line is SHADED THEREFOR, the solution set will be the portion that is shaded in both graphs...the top center portion
300
The solution to the sytem of equations using either substitution or elimination. 6x - 12y = 24 & -x - 6y = 4
What is (2, -1)
300
The solution to the system of equations by graphing: 4x + y = 2 & x - y = 3
What is (1, -2)