How to find the solution to an equation

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Algebra › How to find the solution to an equation

Questions 1 - 10
1

Solve for , given the equation below.

No solutions

Explanation

Begin by cross-multiplying.

Distribute the on the left side and expand the polynomial on the right.

Combine like terms and rearrange to set the equation equal to zero.

Now we can isolate and solve for by adding to both sides.

2

Solve for :

Explanation

First, use the distributive property to simplify the right side of the equation. This gives you

Then, subtract and add to both sides of the equation to get .

3

Solve for x:

None of these

Explanation

Simplify the right side:

Isolate x:

4

Solve for :

None of the other answers

Explanation

To solve for , isolate it from the other variables. First, subtract from both sides to get

.

Then, divide both sides by to get

5

The sum of four consecutive integers equal 98. What is the sum of the smallest and the largest number in the set?

Explanation

Let a variable represent the smallest number in the set. Every consecutive number after the first number will be one unit greater than the other. Then, the four numbers that sum up to 98 are:

where every term in parenthesis represents a number. Add and solve for .

The smallest number is , and the largest number is . Therefore:

The correct answer is:

6

Solve for

None of the other answers.

Explanation

7

Find the solution to this equation:

None of the other answers.

Explanation

To find the solution to this equation you must completely isolate x.

Start by dealing with the parenthesis first. Distribute the 25:

Combine the x terms and move the constant over:

Finally divide the constant away from x to solve:

8

Explanation

Here, . Plug these values in and simplify.

Start with the numerator first:

Then do the same in the denominator:

Finally, combine the two results to find the solution:

9

Solve for :

Explanation

First, use the distributive property to simplify the right side of the equation:

Then, add and subtract from both sides to get

Finally, divide both sides by to get .

10

Solve for :

None of the other answers

Explanation

To solve for , you must isolate it from the other variables. Start by adding to both sides to give you . Now, you need only to divide from both sides to completely isolate . This gives you a solution of .

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