Question 1

Solve using the multiplication principle then graph. -15>-75
Question 2
Translate to an equality. Use the variable x. The number of people in the chess clubi less than or equal to 15.
Question 3
Solve using the addition and multiplication principles 2.1x+20.8>52.0-8.3x The solution set is {x|x>answer}
Question 5
Solve using the multiplication principle 7x>=-6
Question 7
Find the y-intercept and the x-intercept for the equation 2x-3y=30 (Type an ordered pair)
Question 9
Solve using the addition and multiplication principles 6x-9<-33 the solution is {x|x Two different answers}
Question 10
Find the slope if it exists y=-10x+4
Question 11
Graph the following equation and the y-intercept y=x+4. What is the y-intercept??
Question 12
You are taking an English course in which there are four test, each worth 100 points, your have scores of 90, 93, and 97 on the first three tests. You must make a total of 360 in order to get an A. What scores on the last test will give you and A??
Question 13
y-8>-15 the solution is {y|y>answer}
Question 14
Graph the line containing the given pair of points and find the slope.
(-5,1)(0,-2)Find the slope of the line
Question 15
graph the equation by plotting points x=4
Question 16
Use the intercepts to graph the equations 2x-6=3y Use the y intercept when drawingt the lines, If only one intercept exists, use it and another point to draw the line.
Question 17
Solve using the addition principle 2x+5>x+14
Question 18
Graph the equation and identify the y-intercept y=1/2x The y-intercept is??
Question 19
Find the slope, if it exists, x+5y+10
Question 21
Graph the equation and identify the y-intercept 6y+5x=-18 The y-intercept is???
Question 22
Plot (3,-1) on the cordinate axes

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Question 1:

To solve the inequality -15 > -75 using the multiplication principle, we need to divide both sides of the inequality by -1. Since we are dividing by a negative number, the inequality sign will change direction.
(-15)/(-1) > (-75)/(-1)
15 > 75

Since 15 is not greater than 75, the inequality is false.
To graph this inequality, we plot the numbers -15 and -75 on a number line and determine if the solution lies to the left or right of these numbers. In this case, the solution does not exist as the inequality is false.

Question 2:
To translate the statement "The number of people in the chess club is less than or equal to 15" to an equality using the variable x, we can write it as:
x ≤ 15

This inequality represents that the number of people in the chess club (x) is less than or equal to 15.

Question 3:
To solve the inequality 2.1x + 20.8 > 52.0 - 8.3x, we can combine like terms and isolate the variable x on one side of the inequality using addition and multiplication principles.
2.1x + 8.3x > 52.0 - 20.8
10.4x > 31.2

Divide both sides of the inequality by 10.4 to isolate x:
(10.4x)/10.4 > (31.2)/10.4
x > 3

The solution set for this inequality is {x|x > 3}.

Question 5:
To solve the inequality 7x ≥ -6 using the multiplication principle, we need to divide both sides of the inequality by 7. The inequality sign remains the same because 7 is a positive number.
(7x)/7 ≥ (-6)/7
x ≥ -6/7

The solution for this inequality is x ≥ -6/7.

Question 7:
To find the y-intercept and x-intercept for the equation 2x - 3y = 30, we need to set each variable to zero in turn and solve for the other variable.

For the y-intercept, set x = 0:
2(0) - 3y = 30
-3y = 30
y = -10

The y-intercept is (0, -10).

For the x-intercept, set y = 0:
2x - 3(0) = 30
2x = 30
x = 15

The x-intercept is (15, 0).

Question 9:
To solve the inequality 6x - 9 < -33 using the addition and multiplication principles, we can add 9 to both sides of the inequality to isolate x.
6x - 9 + 9 < -33 + 9
6x < -24

Divide both sides of the inequality by 6 to solve for x:
(6x)/6 < (-24)/6
x < -4

The solution for this inequality is {x|x < -4}.

Question 10:
The equation y = -10x + 4 is in the form y = mx + b, where m is the slope and b is the y-intercept. In this equation, the slope is the coefficient of x, which is -10.

Therefore, the slope of the equation y = -10x + 4 is -10.

Question 11:
To graph the equation y = x + 4, we can start by finding the y-intercept. The y-intercept is the value of y when x = 0.
Substitute x = 0 into the equation:
y = 0 + 4
y = 4

Therefore, the y-intercept is (0, 4).

To graph the equation, plot the y-intercept (0, 4) on the coordinate plane and draw a straight line passing through this point.

Question 12:
To score a total of 360 points in the English course with four tests, each worth 100 points, you have scored 90, 93, and 97 on the first three tests.

Let x represent the score on the fourth test. To find the score needed on the fourth test to get an A, we can set up the equation:
90 + 93 + 97 + x = 360

Solve for x by subtracting the sum of the scores received on the first three tests from 360:
90 + 93 + 97 + x = 360
280 + x = 360
x = 360 - 280
x = 80

Therefore, you need a score of 80 on the last test to get an A.

Question 13:
To solve the inequality y - 8 > -15, we can isolate y by adding 8 to both sides of the inequality.
y - 8 + 8 > -15 + 8
y > -7

The solution set for this inequality is {y|y > -7}.

Question 14:
To find the slope of the line passing through the points (-5, 1) and (0, -2), we can use the formula:
slope = (change in y) / (change in x)

Let's calculate the change in y:
-2 - 1 = -3

Next, let's calculate the change in x:
0 - (-5) = 5

Therefore, the slope of the line is (-3) / 5.

Question 15:
To graph the equation x = 4, we plot the point (4, 0) on the coordinate plane. Since x is always equal to 4 in this equation, the line will be a vertical line passing through the point (4, 0).

Question 16:
To graph the equation 2x - 6 = 3y, we can find the x intercept and y intercept.

To find the y intercept, substitute x = 0:
2(0) - 6 = 3y
-6 = 3y
y = -2

The y-intercept is (0, -2).

To find the x intercept, substitute y = 0:
2x - 6 = 3(0)
2x - 6 = 0
2x = 6
x = 3

The x-intercept is (3, 0). We can now plot the y-intercept and x-intercept and draw the line.

Question 17:
To solve the inequality 2x + 5 > x + 14 using the addition principle, we can subtract x from both sides of the inequality to isolate x.
2x + 5 - x > x + 14 - x
x + 5 > 14

Next, subtract 5 from both sides of the inequality:
x + 5 - 5 > 14 - 5
x > 9

The solution for this inequality is {x|x > 9}.

Question 18:
To graph the equation y = (1/2)x, we can identify the y-intercept. In this equation, the y-intercept occurs when x = 0.
Substitute x = 0 into the equation:
y = (1/2)(0)
y = 0

Therefore, the y-intercept is (0, 0).

To graph the equation, plot the y-intercept (0, 0) on the coordinate plane and draw a straight line with a slope of 1/2 passing through this point.

Question 19:
To find the slope of the equation x + 5y + 10, we can rearrange the equation to the slope-intercept form, y = mx + b, where m is the slope.
x + 5y + 10 = 0
5y = -x - 10
y = (-1/5)x - 2

Therefore, the slope of the equation x + 5y + 10 is -1/5.

Question 21:
To graph the equation 6y + 5x = -18 and identify the y-intercept, we can set x = 0 and solve for y.
6y + 5(0) = -18
6y = -18
y = -3

Therefore, the y-intercept is (0, -3).

To graph the equation, plot the y-intercept (0, -3) on the coordinate plane and draw a straight line passing through this point.

Question 22:
To plot the point (3, -1) on the coordinate axes, locate the x-coordinate (3) on the x-axis and the y-coordinate (-1) on the y-axis. Mark the point where the x and y coordinates intersect.