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.

7x - 4 > -5 - x
7x > -5 - x + 4
7x + x > -5 + 4
8x > -1
x > \( \frac{-1}{8} \)
x > -\(\frac{1}{8}\)

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

c² = a² + b²
c² = 5² + 8²
c² = 25 + 64
c² = 89
c = \( \sqrt{89} \)

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\( \sqrt{2} \)

The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:

b² - 12b + 27 = 0
(b - 3)(b - 9) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (b - 3) or (b - 9) must equal zero:

If (b - 3) = 0, b must equal 3
If (b - 9) = 0, b must equal 9

So the solution is that b = 3 or 9

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.

9a⁴ - 6a⁴ = 3a⁴