Select the equation that has infinitely many solutions.(1 point)
Responses
3−3x=−3(x−1)
3 minus 3 x is equal to negative 3 times open paren x minus 1 close paren
3x+5=3x−5
3 x plus 5 is equal to 3 x minus 5
4x+1=4(x+1)
4 x plus 1 is equal to 4 times open paren x plus 1 close paren
3x=2x+1
3x=2x+1
Solve the equation and inequality for x(2 points)
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ax+15=44
: Response area
ax−44<15
: Response area
ax+15=44 can be solved by subtracting 15 from both sides:
ax = 44 - 15
ax = 29
Therefore, the solution is x = 29/a.
For ax-44<15, we can solve it by adding 44 to both sides:
ax < 15 + 44
ax < 59
Therefore, the solution is x < 59/a.
Which inequality represents the graph below:
(1 point)
Responses
3x+7>10
3 x plus 7 is greater than 10
−3x−7≥−10
negative 3 x minus 7 is greater than or equal to negative 10
3x−7<−10
3x−7<−10
−3x+7<10
The inequality that represents the graph below is:
−3x+7<10
(negative 3 x plus 7 is less than 10)
The speed limit sign on the expressway says that the speed limit is 55 mph. Write an equality that represents all speeds you can legally drive on the expressway.(1 point)
Responses
x≥55
x is greater than or equal to 55
x≤55
x is less than or equal to 55
x>55
x is greater than 55
x<55
The equality that represents all speeds you can legally drive on the expressway is:
x≤55
(x is less than or equal to 55)
If you were to graph the inequality below on a number line:
35<7x
(2 points)
Would you use an open or a closed circle?
Would your arrow on the number line point to the left or to the right
To graph the inequality 35<7x on a number line:
1) You would use an open circle because the inequality symbol is '<', indicating that the value of 7x is strictly greater than 35, but not equal to it.
2) The arrow on the number line would point to the right because this indicates that the values of x that satisfy the inequality are greater than the value of 35.
Match the equation to the correct graphed solution.(2 points)
I apologize, but I cannot see the options or graphs you are referring to. Please provide the equations and options for me to match them correctly.
A student solved the following equation using the following steps:
2(2x+2)=4(x+4)
4x+4=4x+4
4=4
Conclusion: Infinitely many solutions
(2 points)
Based on the student's work, the equation was solved correctly or incorrectly
The equation solved correctly would show that it has one, two, three, none or many
solution(s).
Based on the student's work, the equation was solved incorrectly.
The correct equation simplification would be:
4x + 4 = 4x + 8
Therefore, the equation has no solution since the variable (x) cancels out on both sides, resulting in a contradiction (4 = 8), which is not true.
Solve the equation for y:
3x+5y=60
(2 points)
Responses
y=57x5
y is equal to 57 x over 5
y=60−3x
y is equal to 60 minus 3 x
y=60+3x5
y is equal to 60 plus 3 x over 5
y=−35x+12
y is equal to negative 3 fifths x plus 12
To solve the equation 3x+5y=60 for y, we need to isolate the variable y on one side of the equation.
Subtract 3x from both sides:
5y = 60 - 3x
Divide both sides by 5:
y = (60 - 3x)/5
Therefore, the correct solution is y = (60 - 3x)/5.
You originally have x colored pencils in your pencil box. You share them equally between you and your friend. You add in 3 more colored pencils to your own box after sharing them. This gives you a total of 15 pencils.
a) Write an equation and show all of your steps for solving x (the original number of pencils in your box)
b) What if you wanted to have at least 20 pencils left in your box? How many pencils would you have needed originally?
c) Write an inequality and show all steps for solving for x.
a) Let's write an equation based on the given information:
First, you share the colored pencils equally between you and your friend:
(x/2) pencils each.
Then, you add 3 more colored pencils to your own box:
(x/2) + 3 pencils.
Finally, the total number of pencils is 15, so we can write the equation as:
(x/2) + 3 = 15.
To solve for x, we need to isolate x on one side of the equation:
Subtract 3 from both sides:
(x/2) = 15 - 3,
(x/2) = 12.
Multiply both sides by 2 to eliminate the fraction:
x = 2 * 12,
x = 24.
Therefore, the original number of pencils in your box was 24.
b) If you wanted to have at least 20 pencils left in your box, we can modify the equation as follows:
(x/2) + 3 ≥ 20.
To solve for x, we need to isolate x on one side of the inequality:
Subtract 3 from both sides:
(x/2) ≥ 20 - 3,
(x/2) ≥ 17.
Multiply both sides by 2 to eliminate the fraction:
x ≥ 2 * 17,
x ≥ 34.
Therefore, you would have needed at least 34 pencils originally to have at least 20 pencils left in your box.
c) The inequality to represent this situation is:
(x/2) + 3 ≥ 20.
Steps to solve the inequality:
Subtract 3 from both sides:
(x/2) ≥ 17.
Multiply both sides by 2 to eliminate the fraction:
x ≥ 2 * 17,
x ≥ 34.
Therefore, the solution to the inequality is x ≥ 34.
Match the equation to the correct graphed solution.
open circle on -2 going to the left
open circle on 12 going to the left
options
1. 8x < 4x+28
2.-5 (x +5) > -15
3. 1/4 (8x+16)>-4
4. -3 (x - 12)>0
Based on the given information, we can match the equations to the correct graphed solutions as follows:
Open circle on -2 going to the left: This indicates that x = -2 is not included in the solution set and the solution goes to the left from there.
The equation that matches this graphed solution is: 1/4 (8x + 16) > -4.
Open circle on 12 going to the left: This indicates that x = 12 is not included in the solution set and the solution goes to the left from there.
The equation that matches this graphed solution is: -5 (x + 5) > -15.
So, the correct matches are:
1. 1/4 (8x + 16) > -4.
2. -5 (x + 5) > -15.