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.

2x - 9 < 4 - 9x
2x < 4 - 9x + 9
2x + 9x < 4 + 9
11x < 13
x < \( \frac{13}{11} \)
x < 1\(\frac{2}{11}\)

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 + 4)(y + 7)
(y x y) + (y x 7) + (4 x y) + (4 x 7)
y² + 7y + 4y + 28
y² + 11y + 28

The first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:

a² - a + 3 = -2a + 5
a² - a + 3 - 5 = -2a
a² - a + 2a - 2 = 0
a² + a - 2 = 0

Next, factor the quadratic equation:

a² + a - 2 = 0
(a - 1)(a + 2) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (a - 1) or (a + 2) must equal zero:

If (a - 1) = 0, a must equal 1
If (a + 2) = 0, a must equal -2

So the solution is that a = 1 or -2

To combine like terms, add or subtract the coefficients (the numbers that come before the variables) of terms that have the same variable raised to the same exponent.

7a⁷ + 2a⁷ = 9a⁷

According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:

c² = a² + b²
c² = 4² + 8²
c² = 16 + 64
c² = 80
c = \( \sqrt{80} \)