The correct equation to solve for the distance, d, would be:
C: d = St
In physical science, we often use the formula S = d/t to calculate speed.
Suppose your given the speed of a car, S, and time traveled, t, and need to calculate the distance the car traveled.
Which of the following equations would solve for the distance, d?
A: S - t = d
B: S = dt
C: d = St
D: d = s/t
9 answers
-6x + 9 = 4x + 14
To solve the equation -6x + 9 = 4x + 14, we want to isolate the variable x on one side of the equation.
Let's start by getting rid of the constants on both sides. We can do this by subtracting 9 from both sides:
-6x + 9 - 9 = 4x + 14 - 9
Simplifying, we have:
-6x = 4x + 5
Next, let's move all the terms with x to one side by subtracting 4x from both sides:
-6x - 4x = 4x + 5 - 4x
Simplifying, we have:
-10x = 5
Finally, to solve for x, we divide both sides by -10:
-10x / -10 = 5 / -10
Simplifying, we have:
x = -5/10
Simplifying the fraction, we have:
x = -1/2
Therefore, the solution to the equation -6x + 9 = 4x + 14 is x = -1/2.
Let's start by getting rid of the constants on both sides. We can do this by subtracting 9 from both sides:
-6x + 9 - 9 = 4x + 14 - 9
Simplifying, we have:
-6x = 4x + 5
Next, let's move all the terms with x to one side by subtracting 4x from both sides:
-6x - 4x = 4x + 5 - 4x
Simplifying, we have:
-10x = 5
Finally, to solve for x, we divide both sides by -10:
-10x / -10 = 5 / -10
Simplifying, we have:
x = -5/10
Simplifying the fraction, we have:
x = -1/2
Therefore, the solution to the equation -6x + 9 = 4x + 14 is x = -1/2.
Does the equation 8x + 10 = 8x + 10 have one solution, infinite solutions, or no solutions?
The equation 8x + 10 = 8x + 10 is an identity equation. It means that the equation is true for all values of x.
In this case, since the terms on both sides of the equation are exactly the same, no matter what value we substitute for x, the equation will always be true.
Therefore, the equation 8x + 10 = 8x + 10 has infinite solutions.
In this case, since the terms on both sides of the equation are exactly the same, no matter what value we substitute for x, the equation will always be true.
Therefore, the equation 8x + 10 = 8x + 10 has infinite solutions.
how many solutions does 3x + 5 = 3x - 6 have?
The equation 3x + 5 = 3x - 6 simplifies to -11 = -6.
In this case, we end up with a contradiction because the left side of the equation, -11, is not equal to the right side, -6.
Therefore, the equation 3x + 5 = 3x - 6 has no solution.
In this case, we end up with a contradiction because the left side of the equation, -11, is not equal to the right side, -6.
Therefore, the equation 3x + 5 = 3x - 6 has no solution.
how many solutions does 6x + 8 ≥ 2x - 4 have?
To determine the number of solutions for the inequality 6x + 8 ≥ 2x - 4, we need to simplify and solve it.
Let's start by subtracting 2x from both sides of the inequality:
6x - 2x + 8 ≥ 2x - 2x - 4
Simplifying, we have:
4x + 8 ≥ -4
Next, let's subtract 8 from both sides:
4x + 8 - 8 ≥ -4 - 8
Simplifying, we have:
4x ≥ -12
Finally, to solve for x, we divide both sides of the inequality by 4:
(4x) / 4 ≥ -12 / 4
Simplifying, we have:
x ≥ -3
Therefore, the inequality 6x + 8 ≥ 2x - 4 has infinitely many solutions. All values of x greater than or equal to -3 satisfy the inequality.
Let's start by subtracting 2x from both sides of the inequality:
6x - 2x + 8 ≥ 2x - 2x - 4
Simplifying, we have:
4x + 8 ≥ -4
Next, let's subtract 8 from both sides:
4x + 8 - 8 ≥ -4 - 8
Simplifying, we have:
4x ≥ -12
Finally, to solve for x, we divide both sides of the inequality by 4:
(4x) / 4 ≥ -12 / 4
Simplifying, we have:
x ≥ -3
Therefore, the inequality 6x + 8 ≥ 2x - 4 has infinitely many solutions. All values of x greater than or equal to -3 satisfy the inequality.
1 answer