High School Math Solutions – Inequalities Calculator

Symbolab's "getting started" series is moving on to help you solve high school level algebra and calculus.

First up is solving high school level inequalities; that is quadratic inequalities and inequalities involving algebraic fractions.

This is a lot like solving simple inequalities (See Middle School Inequalities post here).
Just like with simple inequalities we start by solving the equation and same as before, we are looking for intervals rather than points.  So what’s the catch?  If you remember, we can’t simply multiply or divide by algebraic factors (multiplying or dividing by negative values reverse the inequality).  Now the two intercepts split the x-axis into three intervals, we have to test the conditions for each. Finally we have to find the intervals that satisfy the condition.

Here's how Symbolab solves quadratic inequality, including the solution steps, (click here):

Here’s an example with algebraic fractions (click here):

Until next time,

Michal

Slope, Distance and More

Ski Vacation? Nope, this is serious stuff; it’s about finding the slope of a line, finding the equation of a line with a given slope, finding the equation of the tangent line to a function, finding the distance between two points, finding the quadrant of a point, finding the midpoint of a line segment.  That’s a lot of lines and points, and functions too.

Basically, you have to follow the rules, no tricks, just knowing how to use it all.   We’ve added the line features to help you sort this through…step by step

Let’s start with a couple of examples.

Find the equation of a line given a point and slope m (click here):

All it takes is solving a linear equation to compute the y=intercept b

Let’s continue with the most challenging one, the tangent line.  It is only challenging b/c it requires derivation, and it is using all the line features we’ve seen so far.  So we have a function and a point, we have to start by finding the slope (that’s where we derivate), compute the slope at a given point, now we can find the tangent line ( slope + point = line)

Here is an example (click here):

You can check out more examples here.

Cheers,
Michal

Middle School Math Solutions - Factoring Calculator

Factoring is another very handy math skill where Symbolab can help you find the solution and also help you learn the solution steps.

Say you have a piece of algebra such as: x^2- 5x+6: the goal of factoring is to get this into a form that looks like (x+u)(x+v).

Why would you want to do that? to break the expression into more manageable chunks.   It turns out to be a super-important step when we come to solve quadratic equations e.g. x ^2 - 5x+6=0  (click here if you want to see how it works ).

The key to factoring quadratic  x^2 - 5x + 6  is to find u and v that factor to 6 and add up to -5.

Here's how the solution looks like (click here):

And here's one more, slightly trickier example (click here):

Feel free to play with more examples on Symbolab until you've properly got the hang of it.

Cheers,

Michal

Middle School Math Solutions – Simultaneous Equations Calculator

Solving simultaneous equations is one small algebra step further on from simple equations. Symbolab math solutions feature can help with this too.

In simultaneous equations there are two or more unknowns.  (In middle school you only need to know how to solve equations with two unknowns. In high school and college you may have to solve for three or more… but that's for later).

If you have two equations and two unknowns - call them x and y - then we're in business;  Symbolab can help you find the solution.

Here's the trick - you use one of the two equations to express x in terms of y, putting the equation in the form x=... Then you substitute for x in terms of y in the second equation. That gives you one equation with one unknown, which we already know how to solve (link back to first blog post).

Here's an example (click here):

And here's another solution (click here):

If you want to take a peek at what's in store in high school math check out how to solve simultaneous equations with three unknowns using the same trick here.


Cheers,

Michal

Middle School Math Solutions – Inequalities Calculator

Next up in our Getting Started maths solutions series is help with another middle school algebra topic - solving simple inequalities.

For example, take an inequality with one unknown x. You have an expression on one side that you know is more or less than what's on the other side.

This is a lot like solving equations (check here). Here too, your goal is to get x by itself on one side and a number on the other.

You do this by adding, subtracting, multiplying or dividing both sides of the inequality. Remember, whatever you do to one side of the inequality, you have to do the same to the other side.  Most important to note is that multiplication or division by a negative number reverses the inequality.

Here's how Symbolab solves it, including the solution steps to help you learn this skill for yourself (click here):

A bit more complicated inequalities might include both lower and upper bounds, or in some cases absolute values.   Here you simply break the inequality into simple inequalities, solve each inequality and combine the solutions (some basic understanding of ‘and’, ‘or’ and ranges is required).

Here’s an example to demonstrate the steps (click here):

Until next time,

Michal

Middle School Math Solutions – Equation Calculator

Welcome to our new "Getting Started" math solutions series. Over the next few weeks, we'll be showing how Symbolab super-easy-to-use math solutions can help you solve math problems in algebra, calculus and more, for students from 6th grade through college and beyond.

As well as giving you the solution, Symbolab also shows you the solution steps, to help you learn the math skills you need.

Let's start with middle school algebra and simple equations. You have an equation with one unknown - call it x. The trick here to solving the equation is to end up with x on one side of the equation and a number on the other. You do this by adding, subtracting, multiplying or dividing both sides of the equation. Remember, whatever you do to one side of the equation, you have to do the same to the other side. (don’t worry, we’ll show you all the steps).

To enter an equation, just use your key pad or Symbolab's special key pad at the top of the screen.

Here's an example of how it works, (click here):

And here's another one which is slightly more complicated - here you have a fraction on one side of the equation; first step is to get rid of it by multiplying both sides of the equation by the number that's underneath the line in the fraction, (click here):

Try some of the other examples that Symbolab suggests on the side of the page until you get the hang of it!

Until next time,

Michal