5(x − 3) − 6(x − 2) > 8x + 2
Responses
A x > 59
x > 5 9
B x < 59
x < 5 9
C x > −59
x > − 5 9
D x < −59
x < − 5 9
E x > −95
To solve the inequality, we will first distribute the terms inside the parentheses:
5(x - 3) - 6(x - 2) > 8x + 2
This becomes:
5x - 15 - 6x + 12 > 8x + 2
Combine like terms:
-x - 3 > 8x + 2
Move all terms containing x to one side of the inequality and all constant terms to the other side:
-x - 8x > 2 + 3
Simplify:
-9x > 5
Divide both sides by -9, remembering to reverse the inequality when dividing by a negative number:
x < -5/9
So the correct response is:
D) x < -59
To solve the inequality 5(x − 3) − 6(x − 2) > 8x + 2, we need to simplify it step-by-step.
First, distribute the 5 and the -6 to the terms inside the parentheses:
5x - 15 - 6x + 12 > 8x + 2
Combine like terms on both sides:
-x - 3 > 8x + 2
Next, move all the terms containing the variable to one side and the constants to the other side. To do that, subtract 8x from both sides:
-x - 3 - 8x > 2
Combine like terms again:
-9x - 3 > 2
Now, move the constant term to the other side by adding 3 to both sides:
-9x > 5
To isolate x, divide both sides by -9. But remember, when you divide an inequality by a negative number, the direction of the inequality symbol is reversed:
x < -5/9
So the correct answer is:
B) x < -5/9
To solve the inequality 5(x − 3) − 6(x − 2) > 8x + 2, we need to simplify the expression and then isolate the variable x.
Let's start by simplifying the expression on both sides of the inequality:
5(x – 3) – 6(x – 2) > 8x + 2
5x – 15 – 6x + 12 > 8x + 2
-x – 3 > 8x + 2
Next, let's combine like terms on both sides of the inequality:
-7 > 9x + 2
To isolate the variable x, we need to move all terms containing x to one side of the inequality. Let's subtract 9x from both sides:
-7 - 9x > 9x - 9x + 2
-7 - 9x > 2x
Next, let's move the constant term (-7) to the other side by adding 7 to both sides:
-7 + 7 - 9x > 2x + 7
-9x > 2x + 7
Now, let's move the 2x term to the left side by subtracting 2x from both sides:
-9x - 2x > 2x - 2x + 7
-11x > 7
Finally, to solve for x, we divide both sides by -11. But we should note that when we divide by a negative number, we need to flip the inequality sign:
-11x / -11 < 7 / -11
x < -7/11
So the solution is x < -7/11.
However, none of the given responses match this solution. It seems there may be a mistake in the answer choices you provided.