Q: Graphs can be valuable tools in algebra because they allow you to display ideas that you'd usually need numbers for in easy-to-understand pictures. Usually, in beginning algebra, graphing problems are restricted to equations with two variables (usually x and y) and are done on a simple 2-D graph with an x axis and a y axis. With these equations, all you need to do is plug in a value for x, then solve for y (or do the reverse) to get two numbers that correspond to a point on the graph. For example, in the equation y = 3x, if we plug in 2 for x, we get y = 6. This means that the point (2,6) (two spaces to the right of center and six spaces above center) is part of this equation's graph. Equations with the form y = mx + b (where m and b are numbers) are especially common in basic algebra. These equations always have a slope of m and cross the y axis at y = b. What do you do when your equation doesn't use an equals sign? Nothing much different than what you'd normally do, it turns out. For inequalities, which use signs like > ("greater than") and < ("less than"), just solve as normal. You'll be left with an answer that's either less than or greater than your variable. For instance, with the equation 3 > 5x - 2, we would solve just like we would for a normal equation: 3 > 5x - 2 5 > 5x 1 > x, or x < 1. This means that every number less than one works for x. In other words, x can be 0, -1, -2, and so on. If we plug these numbers into the equation for x, we'll always get an answer less than 3. One algebra topic that many beginners struggle with is solving quadratic equations. Quadratics are equations with the form ax2 + bx + c = 0, where a, b, and c are numbers (except that a can't be 0.) These equations are solved with the formula x = [-b +/- (b2 - 4ac)]/2a . Be careful the +/- sign means you need to find the answers for adding and subtracting, so you can have two answers for these types of problems. As an example, let's solve the quadratic formula 3x2 + 2x -1 = 0. x = [-b +/- (b2 - 4ac)]/2a x = [-2 +/- (22 - 4(3)(-1))]/2(3) x = [-2 +/- (4 - (-12))]/6 x = [-2 +/- (16)]/6 x = [-2 +/- 4]/6 x = -1 and 1/3 Solving more than one equation at once may sound super-tricky, but when you're working with simple algebra equations, it's not actually that hard. Often, algebra teachers use a graphing approach for solving these problems. When you're working with a system of two equations, the solutions are the points on a graph that the lines for both equations cross at. For example, let's say we're working with a system that contains the equations y = 3x - 2 and y = -x - 6. If we draw these two lines on a graph, we get one line that goes up at a steep angle, and one that goes down at a mild angle. Since these lines cross at the point (-1,-5), this is a solution to the system. If we want to check our problem, we can do this by plugging our answer into the equations in the system a right answer should "work" for both. y = 3x - 2 -5 = 3(-1) - 2 -5 = -3 - 2 -5 = -5 y = -x - 6 -5 = -(-1) - 6 -5 = 1 - 6 -5 = -5 Both equations "check out," so our answer is right!
A: Learn to graph x/y equations. Learn to solve inequalities. Tackle quadratic equations. Experiment with systems of equations.

Q: Diabetes can make finger and toenails more subject to infection. If you have diabetes, or a health condition that decreases your immune system, refrain from cutting your cuticles. Cuticles are there to protect your fingernails and skin. Cuticle clipping is not something you should do every day. Most experts recommend clipping your cuticles in moderation. Stick to clipping your cuticles once every couple of weeks to prevent infections, and soreness near your nail bed. Do not clip off your entire cuticle. The cuticle is a necessary component of the nails that protects them from germs. Only clip off the tips of the cuticles that are comprised of dead skin. Leave the rest intact.
A:
Avoid clipping your cuticles if you have diabetes or other health issues. Clip your cuticles in moderation. Leave some of the cuticle intact.