To factor a quadratic expression, apply the FOIL method (First, Outside, Inside, Last) in reverse. First, find the two Last terms that will multiply to produce 21 as well and sum (Inside, Outside) to equal -10. For this problem, those two numbers are -7 and -3. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² - 10y + 21
y² + (-7 - 3)y + (-7 x -3)
(y - 7)(y - 3)

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

a² - 8a + 15 = 0
(a - 3)(a - 5) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (a - 3) or (a - 5) must equal zero:

If (a - 3) = 0, a must equal 3
If (a - 5) = 0, a must equal 5

So the solution is that a = 3 or 5

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.

a - 4 < \( \frac{a}{7} \)
7 x (a - 4) < a
(7 x a) + (7 x -4) < a
7a - 28 < a
7a - 28 - a < 0
7a - a < 28
6a < 28
a < \( \frac{28}{6} \)
a < 4\(\frac{2}{3}\)

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.

8a - 6a = 2a

A line segment is a portion of a line with a measurable length. The midpoint of a line segment is the point exactly halfway between the endpoints. The midpoint bisects (cuts in half) the line segment.