Directions: Please work out the problems:
Q6: Solve the following equation:
3x + 7 = 2(x + 8)
Q7: Find the Range of the function:
f(x) = 3x + 7 for the domain {-1, 0, 1, 2}
Q8: Find the slope of the graph of the following:
4x – 16y = 20
Slope =
Q9: How many solutions does this system have:
X – 2y = 2
Y = -2x + 5
Q10: Solve the system by either substitution or elimination:
3x – 5y = 21
2x + y = 1
Q6: Solve the equation 3x + 7 = 2(x + 8):
Expand the right side of the equation: 3x + 7 = 2x + 16
Combine like terms: 3x + 7 = 2x + 16
Subtract 2x from both sides: x + 7 = 16
Subtract 7 from both sides: x = 9
Therefore, x = 9 is the solution to the equation.
Q7: Find the Range of the function f(x) = 3x + 7 for the domain {-1, 0, 1, 2}.
To find the range, substitute each value in the domain into the function and list the resulting outputs.
f(-1) = 3(-1) + 7 = 4
f(0) = 3(0) + 7 = 7
f(1) = 3(1) + 7 = 10
f(2) = 3(2) + 7 = 13
The range is {4, 7, 10, 13}.
Q8: Find the slope of the graph of the equation 4x - 16y = 20.
Rearrange the equation in slope-intercept form (y = mx + b), where m is the slope:
-16y = -4x + 20
Divide by -16: y = (1/4)x - 5/4
The coefficient of x, 1/4, is the slope of the graph.
Therefore, the slope is 1/4.
Q9: Determine how many solutions the system of equations has:
x - 2y = 2
y = -2x + 5
To determine the number of solutions, we can compare the slopes of the lines formed by the equations.
The slope of the first equation is 1/2, and the slope of the second equation is -2.
Since the slopes are different, the lines are not parallel, and the system has exactly one solution.
Q10: Solve the system of equations by substitution or elimination:
3x - 5y = 21
2x + y = 1
We can solve the second equation for y and substitute it into the first equation:
2x + y = 1
y = 1 - 2x
Substitute y = 1 - 2x into the first equation:
3x - 5(1 - 2x) = 21
3x - 5 + 10x = 21
13x - 5 = 21
13x = 26
x = 2
Substitute x = 2 into y = 1 - 2x:
y = 1 - 2(2)
y = 1 - 4
y = -3
Therefore, the solution to the system of equations is x = 2 and y = -3.