# Algebra II : Solving Equations

## Example Questions

### Example Question #2382 : Algebra Ii

Solve for :

Explanation:

Before we start with inverse opperations, we need x to be out of the denominator:

First multiply both sides by x- 7.

Next, divide both sides by 4.

Finally, add 7 to both sides.

### Example Question #2383 : Algebra Ii

Solve the following equation for :

and

No real solutions

and

and

Explanation:

Solve the following equation for x:

Begin by factoring the given equation.

We want something of the following form:

Where a and b multiply to get 6 and add to get .

A good place to start would be listing the multiples of 6:1,2,3,6

2 and 3 seem like a good place to start. Since we need negative 5 and positive 6, keeping 2 and 3 negative seem like a good bet.

Because this equation is set equal to zero, we can use the zero product property rule to set each half of our factored equation equal to zero and then solve.

So we have 2 answers:  and

### Example Question #2384 : Algebra Ii

Solve this equation:

Explanation:

Combine  terms by subtracting:

Convert non  terms to decimals or to fractions:

We choose to convert  to a fraction because it is easier.

Simplify and solve for :

### Example Question #2385 : Algebra Ii

Solve:

Explanation:

Since the bases are alike in this problem, taking the log of both sides will eliminate the base  terms.

Take the natural log of both sides.

The equation becomes:

Solve for .

### Example Question #2386 : Algebra Ii

Solve the equation for

Explanation:

Divide both sides by

### Example Question #61 : Solving Equations

Solve the system of equations.

Explanation:

Use elimination, multiply the top equation by -4 so that you can eliminate the X's.

__________________

Combine these two equations, and then you have;

Plug in y into one of the original equations and solve for x.

### Example Question #2387 : Algebra Ii

Find a solution to the following equation:

Explanation:

Find a solution to the following equation:

We can solve for x using basic algebra.

Begin by subtracting 45:

Now, divide by -13 to find the final answer:

### Example Question #61 : Solving Equations

Explanation:

Isolate the term with x:

Simplify:

Isolate x entirely:

### Example Question #2389 : Algebra Ii

Cannot be solved

Explanation:

Square both sides to remove the radical:

Move all terms to the left side and set equal to 0:

Factor the quadratic and set the factors equal to 0:

Solve the factors:

Solve for x: