1) Solve: 8x ¨C (6x + 4) = 8
x = -2
2) -7x > 1/15
the solution set is: {x | x > -105}
3) Solve 5> -4x + 4 or 10 ¡Ü -4x +3
the solution to the inequality is:
[-¡Þ, -7/4] U [-1/4,¡Þ]
4) Use < or > to make the statement true: -9 < 3
5) Graph the inequality on a plane: 5x + 6y ¡Ü 30 not even sure where to start with this one
6)Solve using the multiplication principle.
-5/6x = -7/8
The solution is? 21/20
7) Soybean meal is 14% protein; cornmeal is 7% protein. How many pounds of each should be mixed together in order to get 280-lb mixture that is 11% protein?
How many pounds of the cornmeal should be in the mixture?
How many pounds of the soybean meal should be in the mixture?
how do i solve this?
8) Solve the following system of equations.
X + 9y = 2 (1)
X = 6 ¨C 9y (2)
What is the solution of the system?
9) Solve: 5/2x + 1/4x = 7/4 + x
The solution is x = ?
10) Find the slope, if it exists, of the line containing the pair of points
(8,1) and (10,-6)
The slope m = ?
1) To solve the equation 8x - (6x + 4) = 8, we need to simplify the expression on the left side. By distributing the negative sign to both terms inside the parentheses, we get:
8x - 6x - 4 = 8
Combine like terms:
2x - 4 = 8
Now, isolate the variable by adding 4 to both sides of the equation:
2x = 12
Finally, divide both sides by 2 to solve for x:
x = 6
Therefore, the solution to the equation is x = 6.
2) To solve the inequality -7x > 1/15, we need to isolate the variable x. First, divide both sides by -7, but remember to reverse the inequality sign when dividing by a negative number:
x < (1/15) / -7
Simplify:
x < -1/105
Therefore, the solution set is {x | x > -1/105}.
3) To solve the inequality 5 > -4x + 4 or 10 ≤ -4x + 3, we need to find the values of x that satisfy either of the two inequalities.
For the first inequality, subtract 4 from both sides:
1 > -4x
Divide both sides by -4 (don't forget to reverse the inequality sign):
x < 1/4
For the second inequality, subtract 3 from both sides:
7 ≤ -4x
Divide both sides by -4 (again, reverse the inequality sign):
x ≥ -7/4
Therefore, the solution to the inequality is [-∞, -7/4] U [1/4, ∞].
4) To make the statement -9 < 3 true, we need to change the less than sign (<) to a greater than sign (>).
Therefore, -9 > 3 is the correct statement.
5) To graph the inequality 5x + 6y ≤ 30 on a plane, we need to first rewrite it in slope-intercept form (y = mx + b) to identify the slope and y-intercept.
Rearranging the inequality, we get:
6y ≤ -5x + 30
Divide both sides by 6 to simplify:
y ≤ (-5/6)x + 5
Now we can plot the graph by starting at the y-intercept (0, 5) and using the slope (-5/6) to find other points on the line. We draw a solid line for "≤" and shade the area below the line to represent the solutions to the inequality.
6) To solve the equation -5/6x = -7/8 using the multiplication principle, we need to isolate the variable x. First, multiply both sides by -6/5 (the reciprocal of -5/6) to eliminate the fraction on the left side:
(-6/5)(-5/6)x = (-6/5)(-7/8)
Simplify by canceling out common factors:
x = 21/20
Therefore, the solution to the equation is x = 21/20.
7) To determine how many pounds of soybean meal and cornmeal should be mixed to achieve a 280-lb mixture that is 11% protein, we can set up a system of equations.
Let x be the number of pounds of soybean meal and y be the number of pounds of cornmeal.
The total weight equation is given by:
x + y = 280
The protein equation is given by:
0.14x + 0.07y = 0.11(280)
Simplifying the second equation:
0.14x + 0.07y = 30.8
Now you can use either substitution or elimination to solve the system of equations.
8) The given system of equations is:
x + 9y = 2 (1)
x = 6 - 9y (2)
Since equation (2) is already solved for x, you can substitute the expression 6 - 9y for x in equation (1):
6 - 9y + 9y = 2
Simplify:
6 = 2
This equation has no solution. The system of equations is inconsistent.
9) To solve the equation 5/2x + 1/4x = 7/4 + x, we need to combine like terms and isolate the variable. First, find a common denominator for the fractions:
(10/4)x + (1/4)x = 7/4 + (4/4)x
Simplify the left side:
(11/4)x = (7 + 4/4)x
Combine the right side:
(11/4)x = (11/4)x
Since the x terms are already the same on both sides, the equation holds true for any value of x.
Therefore, the solution is that x can be any real number.
10) To find the slope of the line containing the points (8, 1) and (10, -6), we can use the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the given coordinates:
m = (-6 - 1) / (10 - 8) = -7 / 2
Therefore, the slope (m) of the line is -7/2.