To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the < sign and the answer on the other.

2a + 8 < \( \frac{a}{-2} \)
-2 x (2a + 8) < a
(-2 x 2a) + (-2 x 8) < a
-4a - 16 < a
-4a - 16 - a < 0
-4a - a < 16
-5a < 16
a < \( \frac{16}{-5} \)
a < -3\(\frac{1}{5}\)

To multiply binomials, use the FOIL method. FOIL stands for First, Outside, Inside, Last and refers to the position of each term in the parentheses:

(y + 5)(y - 8)
(y x y) + (y x -8) + (5 x y) + (5 x -8)
y² - 8y + 5y - 40
y² - 3y - 40

To find the diagonal we need to know the length of one of the square's sides. We know the area and the area of a square is the length of one side squared:

a = s²

so the length of one side of the square is:

s = \( \sqrt{a} \) = \( \sqrt{49} \) = 7

The Pythagorean theorem defines the square of the hypotenuse (diagonal) of a triangle with a right angle as the sum of the squares of the other two sides:

c² = a² + b²
c² = 7² + 7²
c² = 98
c = \( \sqrt{98} \) = \( \sqrt{49 x 2} \) = \( \sqrt{49} \) \( \sqrt{2} \)
c = 7\( \sqrt{2} \)

To multiply monomials, multiply the coefficients (the numbers that come before the variables) of each term, add the exponents of like variables, and multiply the different variables together.

(3a)(5ab) - (5a²)(8b)
(3 x 5)(a x a x b) - (5 x 8)(a² x b)
(15)(a¹⁺¹ x b) - (40)(a²b)
15a²b - 40a²b
-25a²b

You need to find the value of c so solve the first equation in terms of x:

8c + x = -6
x = -6 - 8c

then substitute the result (-6 - 8c) into the second equation:

8c - 2(-6 - 8c) = 1
8c + (-2 x -6) + (-2 x -8c) = 1
8c + 12 + 16c = 1
8c + 16c = 1 - 12
24c = -11
c = \( \frac{-11}{24} \)
c = -\(\frac{11}{24}\)