Equations & Expressions
Simplify: 3(2x + 4) - 4(x - 5)
Answer: 2x + 32
Solve by graphing: y = 2x + 1 and y = -x + 4.
Answer: (1, 3)
A taxi charges $10 plus $3 per mile. Write the equation for C.
Answer: C = 10 + 3m
Find the slope of the line through (0, 2) and (4, 6).
Answer: Slope = 1
Solve for x: 4x + 3y = 12.
Answer: x = (12 - 3y)/4 or 3-(3/4)y
Which equations are equivalent to 2(3x - 5) - 4 = 10?
A) 6x - 14 = 10
B) 6x - 10 = 14
C) 6x - 4 = 10
Answer: A) 6x - 14 = 10 and B) 6x - 10 = 14
Solve by substitution: y = 3x - 2 and 2x + y = 7.
Answer: x = 9/5, y = 17/5
A cafeteria budget is $200 for $5 meals. Solve for the number of meals.
Answer: n = 40
Graph y = -3/2x + 3. Find the x-intercept.
Answer: x = 2
Solve for b: A = 1/2bh.
Answer: b = 2A/h
Solve for x: 4(2x - 3) = 3x + 9.
Answer: x = 21/5
Solve by elimination: 2x + 3y = 12 and x - 3y = 6.
Answer: x = 6, y = 0
A gym charges $30 to join and $10/month. Write the equation for C.
Answer: C = 30 + 10m
Write the equation of a line with slope -2 through (0, 5).
Answer: y = -2x + 5
Solve for b: 5a - 2b = c.
Answer: b = (5a - c)/2
Select all equations equivalent to 2(5x + 6) = 3(4x + 2):
A) 10x + 12 = 12x + 6
B) 10x - 6 = 12x - 12
C) 2x + 6 = 2x + 6
Answer: A) 10x + 12 = 12x + 6
and
B) 10x - 6 = 12x - 12
Solve algebraically using any method: 3x - y = 5 and 2x + y = 11.
Answer: x = 3.2, y = 4.6
or
x = 16/5, y =23/5
A pizza costs $10 plus $1.50 per topping. Find the cost for 6 toppings.
Answer: C = 19
A line has slope 3/4 and y-intercept -2. Write its equation.
Answer: y = 3/4x - 2
Solve for x: 2x + 5y = 10.
Answer: x = (10 - 5y)/2
Select all equations equivalent to 3(4x - 5) = 2(6x + 1):
A) 12x - 15 = 12x + 2
B) 12x - 15 = 12x - 2
C) 12x - 11 = 12x + 6
Answer: A) 12x - 15 = 12x + 2
and C) 12x - 11 = 12x + 6
Solve by elimination: 8x - 3y = 10 and 5x + 6y = 22.
Answer: x = 2, y = 2
A phone plan costs $12 plus $0.05 per minute. If the bill is $22, find the minutes used.
Answer: m = 200
A line passes through (-6, 4) and (2, -2). Find the slope and equation.
Answer: Slope = -3/4, y = -3/4x - 1/2
Solve for b: 3b - 4a = c.
Answer: b = (c + 4a)/3