Algebraic Expressions & Simplifying
Identify the coefficient of x and the constant term in the expression: 7x - 12
Coefficient of x: 7
Constant term: -12
Solve for x:
x + 7 = 19
x = 12
A line rises 6 units when it runs 3 units to the right.
What is the slope?
What does the solution of a system of equations represent graphically?
The point where the two lines intersect
Is the pattern linear or quadratic?
2, 6, 12, 20
Quadratic (second differences are constant)
Simplify:
4a + 7 - 2a + 5
2a + 12
Solve for x:
4x - 9 = 23
x = 8
Write the equation of a line with slope 3 and y-intercept –5.
y = 3x - 5
Solve graphically:
y = x + 2
y = x - 1
No solution (parallel lines)
Factor:
x2 + 7x + 12
Evaluate the expression when x = -2:
3x2 - 4x + 1
= 12 + 8 + 1
= 21
Solve for x:
5x + 6 = 2x + 18
x = 4
Find the equation of the line that passes through (2,1) with slope –2.
y - 1 = -2(x - 2)
y = -2x + 5
Solve using substitution:
y = 2x + 1
y = x + 4
2x + 1 = x + 4
x = 3, y = 7
Factor completely:
2x2 - 8x
2x(x - 4)
Expand and simplify:
5(2x - 3) - 4(x + 1)
= 6x - 19
A number increased by 8 is three times the number minus 4. Find the number.
x + 8 = 3x - 4
x = 6
A taxi charges a $4 flat fee plus $2.50 per kilometre. Write an equation to model the cost C.
C = 2.5k + 4
Solve using elimination:
2x + y = 11
x + y = 8
x = 3, y = 5
Solve by factoring:
x2 - 9x + 20 = 0
(x - 5)(x - 4) = 0
x = 4, 5
Simplify completely:
2(3x - 4) + 5x - 3(x + 6)
= 6x - 8 + 5x - 3x - 18
= 6x - 26
Solve for x:
(2x - 5)/3 = (x + 4)/2
x = 22
Line A: y = 1.5x + 6
Line B: y = 2.5x + 1
Which line increases faster and why?
Line B, because it has the greater slope (2.5 > 1.5).
A total of 50 coins are made up of loonies ($1) and toonies ($2). The total value is $78.
How many of each coin are there?
x + y = 50
x + 2y = 78
22 loonies, 28 toonies
A quadratic relation has its vertex at (3,−2). What is the minimum value of the relation?
-2