Solving for the Variable

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GED Math › Solving for the Variable

Questions 21 - 30
21

Solve:

Explanation

Step 1: Move the constant from the left to the right:

Step 2: Simplify:

Step 3: Divide by the coefficient on the left hand side to both sides of the equation:

Simplify:

Step 4: Take the square root of both sides:

Simplify:

22

Solve:

Explanation

Add six on both sides.

Divide by 7 on both sides.

The answer is:

23

Solve:

Explanation

To isolate the x-variable, we will need to multiply by one-third on both sides.

The answer is:

24

Solve for :

Explanation

In order to solve for , we will need the equation to be in terms of , and isolate the variable .

Solve by grouping the terms together. Subtract on both sides.

Divide by negative five on both sides.

The answer is:

25

Which of the following is the solution set of the inequality ?

Explanation

Solve using the properties of inequality, as follows:

Note that division by a negative number reverses the symbols.

In interval form, this is .

26

Solve for :

Explanation

27

If , then

Explanation

To solve this you must find the value of .

The first equation states that . This is a mult-step equation. The first step is to remove the constant, 6, from the equation; this is done by using the inverse operation, which means you would subtract the 6 from both sides of the equation.

Then divide both sides by the 7 in order to isolate the variable.

Then plug the 3 into the second equation for the value of x.

28

Give the solution set:

Explanation

Collect the like terms by subtracting from both sides:

Isolate on the right by dividing both sides by . Reverse the direction of the inequality symbol, since you are dividing by a negative number:

The solution set is .

29

Solve for the variable:

Explanation

Subtract from both sides.

Add 3 on both sides.

The answer is:

30

Which of the following makes this equation true:

Explanation

To answer this question, we will solve for y. We get

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