Algebra two homework help

Algebra two homework help

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Rational Reasoning IMathAS

This is called an equation. The number is the solution to the equation. One of the first procedures used in solving equations has an application in our everyday world. Suppose that we place a 10 -kilogram box on one side of a seesaw and a 10 -kilogram stone on the other side. If the center of the box is the same distance from the balance point as the center of the stone, algebra two homework help, we would expect the seesaw to balance.

The box and the stone do not look the same, but they have the same value in weight. If we add a 2 -kilogram lead weight to the center of weight of each object at the same time, the seesaw should still balance.

The results are equal. There is a similar principle in mathematics. We can state it in words like this. If the same number is added to both sides of an equation, the results on each side are equal in value. Here is an example. EXAMPLE 1 Solve for x. We have just found the solution of the equation. The solution is a value for the variable that makes the equation true.

We then say that the value, 4in our example, satisfies the equation. We can easily verify that 4 is a solution by substituting this value in the original equation. This step is called checking the solution.

When the same value appears on both sides of the equals sign, we call the equation an identity. Because the two sides of the equation in our check have the same value, we know that the original equation has been correctly solved.

We have found the solution, algebra two homework help. When you are trying to solve these types of equations, you notice that you must add a particular number to both sides of the equation.

What is the number to choose? Look at the number that is on the same side of the equation with xthat is, the number added to x. Then think of the number that is opposite in sign. This is called the additive inverse of the number. The additive inverse of 16 is The additive inverse of -3 is 3.

The number to add to both sides of the equation is precisely this additive inverse. It does not matter which side of the equation contains the variable. The x term may be on the right or left. In the next example the x term will algebra two homework help on the right. EXAMPLE 2 Solve for x. This will eliminate the -3 on the right and isolate x. It checks.

Before you add a number to both sides, you should always simplify the equation. The following example shows how combining numbers by addition separately, algebra two homework help, on both sides of the equation—simplifies the equation.

EXAMPLE 3 Solve for x. The value of x is In Example 3 we added -5 to each side. You could subtract 5 from each side and get the same result. In earlier lesson we discussed how subtracting a 5 is the same as adding a negative 5. Do you see why? We can determine if a value is the solution to an equation by following the same steps used to check an answer.

Substitute the value to be tested for the variable in the original equation. We will obtain an identity if the value is the solution. If it is not, find the solution. We substitute 10 for x in the equation algebra two homework help see if we obtain an identity. It is not an identity. Now we take the original equation and solve to find the solution. We must be especially careful to write the correct sign for each number when solving equations.

To combine the fractions, the fractions must have common denominators. The least common denominator LCD of the fractions is What would happen if we multiplied algebra two homework help side of an equation by the same number?

For example, what would happen if we multiplied each side of an equation by 3? If we triple the number of weights on each side we are multiplying each side by 3the seesaw should still balance. Multiplication Principle If both sides of an equation are multiplied by the same number, the results on each side are equal in value, algebra two homework help. In symbols we can restate the multiplication principle this way.

Let us look at an equation where it would be helpful to multiply each side of the equation by 3. We will multiply each side of algebra two homework help equation by 3because we want to isolate the variable x. Try it. Then check your solution.

Thus, it would seem that the multiplication principle would allow us to divide each side of the equation by any nonzero real number. Is there a real-world example of this idea? Suppose that we were to cut the two objects in half so that the amount of weight of each was divided by 2. We then return the objects to the same places on the seesaw. The seesaw would still balance. Division Principle If both sides of an equation are divided by the same nonzero number, the results on each side are equal in value.

Note : We put a restriction algebra two homework help the number by algebra two homework help we are dividing. We cannot divide by zero. Thus we restrict our divisor to nonzero numbers. We can restate the division principle this way. The solution is We look at the side of the equation that contains x. We notice the number that is multiplied by x.

We divide by that number. The division principle tells us that we can still have a true equation provided that we divide by that number on both sides of the equation. The solution to an equation may be a proper fraction or an improper fraction, algebra two homework help. If you leave the solution as a fraction, it will be easier to check that solution in the original equation.

In examples 2 and 3 we divided by the number multiplied by x the coefficient of x. This procedure is followed regardless of whether the sign of that number is positive or negative.

EXAMPLE 4 Solve for x. The coefficient of x may be 1 or You may have to rewrite the equation so that the coefficient of 1 or -1 is obvious. EXAMPLE 5 Solve for x. Now the coefficient of -1 is obvious. Solve equations in which the variable appears on both sides of the equation. To solve many equations, we must use both the addition principle and the multiplication principle.

EXAMPLE 1 Solve for x and check your solution. A Variable on Both Sides of the Equation. In some cases the variable appears on both sides of the equation. We would like to rewrite the equation so that all the terms containing the variable appear on one side, algebra two homework help. To do this, we apply the addition principle to the variable term.

Many problems have variable terms and constant terms on both sides of the equation. You will want to get all the variable terms on one side and all the constant terms on the other side. EXAMPLE 3 Solve for x and check your solution. Algebra two homework help our next example we will study equations that need simplifying before any other steps are taken. Where it is possible, you should first collect like terms on one or both sides of the equation, algebra two homework help.

The variable terms can be collected on the right side or the left side, algebra two homework help.

4.3 Algebra 2 Homework Help

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Math homework help. Hotmath explains math textbook homework problems with step-by-step math answers for algebra, geometry, and calculus. Online tutoring available for math help The blogger.com site was retired on August 11th, as part of a continuous effort to provide you with the most relevant and up to date content Free math lessons and math homework help from basic math to algebra, geometry and beyond. Students, teachers, parents, and everyone can find solutions to their math problems instantly