-4(5y + 17) < -24y – 32
To simplify the given inequality, let's distribute the -4 on the left side:
-4(5y + 17) < -24y - 32
-20y - 68 < -24y - 32
Now, let's move all the y terms to one side and the constant terms to the other side:
-20y + 24y < -32 + 68
4y < 36
Finally, divide both sides of the inequality by 4:
y < 9
So the solution to the given inequality is y < 9.
Write the English phrase as a mathematical inequality.
The snowfall,
h
, in Monroe County is between
2
inches and
5
inches.
The phrase can be represented by the inequality
2 inches ≤ h ≤ 5 inches
To solve this inequality, we'll begin by simplifying both sides step by step.
1. Distribute the multiplication on the left side:
-4 * 5y = -20y
-4 * 17 = -68
The inequality becomes:
-20y - 68 < -24y - 32
2. Combine like terms on both sides:
-20y + 24y < -32 + 68
On the left side, -20y + 24y simplifies to 4y.
The inequality becomes:
4y < 36
3. Divide both sides by 4 to isolate the variable y:
(4y) / 4 < 36 / 4
The inequality becomes:
y < 9
Therefore, the solution to the inequality -4(5y + 17) < -24y – 32 is y < 9.
To solve this inequality, you'll need to distribute the -4 on the left side of the equation.
First, distribute -4 to both terms within the parentheses:
-4 * 5y = -20y
-4 * 17 = -68
The inequality becomes:
-20y - 68 < -24y - 32
Next, we need to isolate the variable term on one side of the inequality. Let's start by moving the -24y term to the left side of the inequality by adding 24y to both sides:
-20y - 24y - 68 < -32
Combine like terms on the left side:
-44y - 68 < -32
Now, let's get rid of the constant term on the left side. Add 68 to both sides:
-44y - 68 + 68 < -32 + 68
Simplifying further, we get:
-44y < 36
Finally, to isolate y, divide both sides by -44. Remember that when dividing an inequality by a negative number, you need to reverse the inequality symbol.
-44y / -44 > 36 / -44
Simplifying the equation:
y > -(36/44)
The final answer is:
y > -9/11.