Linear and Nonlinear Expressions in x
The product of a number and ten.
What is a linear expression?
10n
5x - 2 = 8
What is x = 2?
5x - 2 = 8
5x = 10
x = 2
7x - 3 = 5x + 5
What is one solution (unique solution)?
7x - 3 = 5x + 5
2x = 8
x = 4
A train travels at a constant rate of 45 miles per hour.
What is C = 45 / 1?
The point (4, -3) is or is not a solution to the linear equation 2x + y = 5.
The point (4, -3) is a solution to the linear equation 2x + y = 5.
2x + y = 5
2(4) + (-3) = 5
8 + (-3) = 5
5 = 5
The sum of four consecutive numbers.
What is a linear expression?
x + (x + 1) + (x + 2) + (x + 3)
7x - 4 + x = 12
What is x = 2?
7x - 4 + x = 12
8x - 4 = 12
8x = 16
x = 2
11x - 2x + 15 = 8 + 7 + 9x
What is infinitely many solutions?
11x - 2x + 15 = 8 + 7 + 9x
9x + 15 = 15 + 9x
Carlos walks 4 miles every night for exercise. It takes him exactly 63 minutes to finish his walk.
What is C = 4 / 63?
The linear equation represents the graph of the line defined by the equation ax + by = c, where a = 0, b = 1, and c = -5.
What is y = -5?
ax + by = c
(0)x + (1)y = -5
0 + 1y = -5
y = -5
The square of a number times six.
What is a nonlinear expression?
6n2
3x + 2 - x = 11x + 9
What is x = -7/9?
3x + 2 - x = 11x + 9
2x + 2 = 11x + 9
-7 = 9x
-7/9 = x
3(x - 14) + 1 = -4x + 5
What is one solution (unique solution)?
3(x - 14) + 1 = -4x + 5
3x - 42 + 1 = -4x + 5
3x - 41 = -4x + 5
7x = 46
46/7 = x
The linear equation in two variables that represents a car assembled at a constant rate on an assembly line in 6 hours.
What is y = (1/6)x?
C = 1 car / 6 hours
y = (1/6)x
The linear equation represents the graph of the line defined by the equation ax + by = c, where a = 1, b = 0, and c = -8.
What is x = -8?
ax + by = c
(1)x + (0)y = -8
1x + 0 = -8
x = -8
Triple the sum of a number and twenty.
What is a linear expression?
3(n + 20)
5x - (x + 3) = 1/3 (9x + 18) - 5
What is x = 4?
5x - (x + 3) = 1/3 (9x + 18) - 5
5x - x - 3 = 3x + 6 - 5
4x - 3 = 3x + 1
x = 4
-3x + 32 - 7x = -2(5x + 10)
What is no solution?
-3x + 32 - 7x = -2(5x + 10)
-10x + 32 = -10x + 8
32 does not equal 8
The number of gallons water leaks from a faucet after one hour when it leaks at a constant rate of 1/3 gallons per minute.
What is 20 gallons?
C = 1/3 gallons / 1 minute
y = (1/3) x
y = (1/3)(60)
y = 20
The linear equation represent the graph of the line that coincides with the x-axis?
y = 0
y = 0 is the x-axis
The cube of a number divided by two.
What is a nonlinear expression?
n3 / 2
7x + 8(x + 1/4) = 3(6x - 9) - 8
What is x = 37/3?
7x + 8(x + 1/4) = 3(6x - 9) - 8
7x + 8x + 2 = 18x - 27 - 8
15x + 2 = 18x - 35
37 = 3x
37 / 3 = x
1/2 (8x + 26) = 13 + 4x
What is infinitely many solutions?
1/2 (8x + 26) = 13 + 4x
4x + 13 = 13 + 4x
The number of minutes it takes a copy machine to make 24 copies at a constant rate of 80 copies in 2.5 minutes.
What is 45 minutes?
C = 80 / 2.5
y = 80/2.5 x
24 = (80 / 2.5)x
The linear equation represents the graph of the line that coincides with the y-axis?
x = 0
x = 0 is the y-axis