Solving Linear Equations
Solve for x: x + 10 = 2
x = -8
The general equation of a line in slope-intercept form
y = mx + b
The simplified form of y3 x y5
y8
Solve for x: 4(x + 2) - 10 = 2x + 16
A gym membership has an initial sign-up fee and a monthly cost. John pays a total of $100 for the first month and $140 for the second month. If the monthly cost is constant, what is the initial sign-up fee?
$60
c = -4
The slope (m) of a horizontal line
0
The value of any non-zero number raised to the power of zero
1
How many solutions does the equation 5x + 3 = 5x + 7 have?
No solutions
A vending machine only accepts quarters and dimes. Sarah counted a total of 15 coins in the machine, and their total value is $2.55. How many quarters and how many dimes are there?
There are 7 quarters and 8 dimes
Solve for y: 3 (y + 4) = 8y - 3
y = 3
The slope of the line that passes through the points (2, 6) and (4, -3)
- 9/2 or -4.5
The simplified form of (y3)4
y12
Solve the following system of equations for both x and y:
Equation 1: y = x + 3
Equation 2: 2x + y = 18
x = 5, y = 8
Two cars leave the same location traveling in opposite directions. Car A travels at 55 mph. Car B travels at 65 mph. How many hours will it take for them to be 480 miles apart?
4 hours or t = 4
Solve for k: k/4 - 3 = 0
The equation of the line that has a slope of 6 and a y-intercept of -1
y = 6x - 1
Simplify the expression (x3 x x5)2
x16
Write a linear equation in the form y=mx+b that represents a situation where a plumber charges a flat service fee of $40 plus $75 for every hour of work (h). Let C be the total cost.
A number is increased by 5, and that sum is multiplied by 4. The result is 56. What is the original number?
9
Solve for d: -4d + 2(3 + d) = -14
d = 10
The equation of the line passing through points (4, 2) and (5, 7) in slope-intercept form.
y = 5x - 18
Simplify the expression 12y7/4y7 (where y is not equal to 0)
3
Solve the inequality for x: -3x + 4 ≤ 16
x ≥ -4
The length of a rectangular garden is 10 feet. The homeowner wants the total area of the garden to be at least 80 square feet. Write and solve an inequality to find the possible widths (w) of the garden.
w ≥ 8