Solve the equation and inequality for x.
ax + 15 = 44: ?
ax − 44 < 15: ?
To solve the equation ax + 15 = 44 for x, we need to isolate x.
Starting with the given equation:
ax + 15 = 44
Subtracting 15 from both sides:
ax = 44 - 15
ax = 29
Dividing both sides by a:
x = 29/a
So the solution for the equation ax + 15 = 44 is x = 29/a.
To solve the inequality ax - 44 < 15 for x, we need to isolate x.
Starting with the given inequality:
ax - 44 < 15
Adding 44 to both sides:
ax < 15 + 44
ax < 59
Dividing both sides by a:
x < 59/a
So the solution for the inequality ax - 44 < 15 is x < 59/a.
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.
x ≤ 55
x ≥ 55
x > 55
x < 55
The equality that represents all speeds you can legally drive on the expressway, given that the speed limit is 55 mph, is:
x ≤ 55
If you were to graph the inequality below on a number line:
35 < 7x
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, you would use an open circle and the arrow would point to the right.
The open circle indicates that 35 is not included in the solution set, as the inequality is strict (35 < 7x, not 35 ≤ 7x).
The arrow pointing to the right indicates that the solution set includes all values greater than the solution. In this case, x would be all values greater than 35/7, or 5.
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
Based on the student's work, the equation was solved ?
The equation solved correctly would show that it has ? solution(s).
Based on the student's work, the equation was solved incorrectly.
The equation they started with is: 2(2x + 2) = 4(x + 4)
However, the next step they wrote is incorrect. It should be:
4x + 4 = 4x + 8
By expanding and simplifying the equation correctly, we get:
4x + 4 = 4x + 8
Subtracting 4x from both sides, we get:
4 = 8
This is a contradiction, as 4 cannot equal 8. Therefore, there are no solutions to this equation.
Conclusion: The equation has no solution.
Solve the equation for y:
3x + 5y = 60
y = 60 + 3x/5
y = 57x/5
y = −3/5x + 12
y = 60 − 3x
To solve the equation 3x + 5y = 60 for y, we need to isolate y on one side of the equation.
Starting with the given equation:
3x + 5y = 60
Subtracting 3x from both sides:
5y = 60 - 3x
Dividing both sides by 5:
y = (60 - 3x)/5
So the solution for y is y = (60 - 3x)/5.
To solve the equation ax + 15 = 44 for x, we need to isolate x on one side of the equation.
Step 1: Subtract 15 from both sides of the equation:
ax + 15 - 15 = 44 -15
ax = 29
Step 2: Divide both sides of the equation by a to solve for x:
ax/a = 29/a
x = 29/a
Therefore, the solution for the equation ax + 15 = 44 is x = 29/a.
Now, let's move on to solving the inequality ax - 44 < 15 for x.
Step 1: Add 44 to both sides of the inequality:
ax - 44 + 44 < 15 + 44
ax < 59
Step 2: Divide both sides of the inequality by a to solve for x.
ax/a < 59/a
x < 59/a
Therefore, the solution for the inequality ax - 44 < 15 is x < 59/a.