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- Ecuaciones lineales con variables en ambos lados. ¿Por qué hacemos lo mismo a ambos lados? : variable en ambos lados. (Abre un modal) Introducción a las ecuaciones con variables en ambos lados.
- Ecuaciones lineales con paréntesis. Ecuaciones con paréntesis. (Abre un modal) Razonar con ecuaciones lineales. Repaso de ecuaciones de varios pasos.
- Analizar el número de soluciones de ecuaciones lineales. Cantidad de soluciones a ecuaciones. (Abre un modal) Ejemplo resuelto: número de soluciones de las ecuaciones.
- Ecuaciones lineales con coeficientes desconocidos. (Abre un modal) ¿Por qué es importante aprender álgebra?
- Solving
- How to Solve
- Safe Things to Do
- Adding Or Subtracting A Value
- What If I Solve It, But "X" Is on The Right?
- Multiplying Or Dividing by A Value
- Multiplying Or Dividing by Variables
- Summary
Our aim is to have x (or whatever the variable is) on its ownon the left of the inequality sign: We call that "solved".
Solving inequalities is very like solving equations... we do most of the same things ... ... but we must also pay attention to the direction of the inequality. Direction: Which way the arrow "points"
These things do not affectthe direction of the inequality: 1. Add (or subtract) a number from both sides 2. Multiply (or divide) both sides by a positivenumber 3. Simplify a side But these things do change the directionof the inequality ("<" becomes ">" for example): Here are the details:
We can often solve inequalities by adding (or subtracting) a number from both sides (just as in Introduction to Algebra), like this:
No matter, just swap sides, but reverse the signso it still "points at" the correct value! Note: "x" canbe on the right, but people usually like to see it on the left hand side.
Another thing we do is multiply or divide both sides by a value (just as in Algebra - Multiplying). But we need to be a bit more careful (as you will see).
Here is another (tricky!) example: To help you understand, imagine replacing b with 1 or −1 in the example of bx < 3b: 1. if b is 1, then the answer is x < 3 2. but if b is −1, then we are solving −x < −3, and the answer is x > 3 The answer could be x < 3 orx > 3 and we can't choose because we don't know b.
Many simple inequalities can be solved by adding, subtracting, multiplying or dividing both sides until you are left with the variable on its own.But these things will change direction of the inequality:Don't multiply or divide by a variable(unless you know it is always positive or always negative)Let's explore some different ways to solve equations and inequalities. We'll also see what it takes for an equation to have no solution, or infinite solutions.
En esta unidad, estudiamos desigualdades como x+2y>5 y las graficamos. Esto nos ayuda a ver sus soluciones. También exploramos sistemas de desigualdades (varias desigualdades al mismo tiempo) y las usamos para describir situaciones del mundo real.
Aprende sobre las ecuaciones y desigualdades que contienen variables. En estas lecciones nos enfocamos en la resolución de ecuaciones y en entender las soluciones de las desigualdades.
Obtén más información sobre inecuaciones con nuestro solucionador matemático gratuito, que incluye soluciones paso a paso.
Linear equations and inequalities: Unit test About this unit We will now equate two algebraic expressions and think about how it might constrain what value the variables can take on.
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