How to solve one-step equations

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Math › How to solve one-step equations

Questions 1 - 10
1

Solve for if

Explanation

To solve for we must get all of the numbers on the other side of the equation as .

To do this in a problem where is being divided by a number, we must multiply both sides of the equation by the number.

In this case the number is so we multiply each side of the equation by to make it look like this

The 's on the left side cancel so we only have .

Then we perform the necessary multiplication to get the answer of .

2

What is ?

Explanation

To get rid of a fraction, we multiply by the reciprocal. So we take and multiply both sides by :

and cancel each other out, so we are left with or .

3

Solve for if

Explanation

To solve for we must get all of the numbers on the other side of the equation of .

To do this in a problem where a number is being added to , we must subtract the number from both sides of the equation.

In this case the number is so we subtract from each side of the equation to make it look like this

To subtract fractions we must first ensure that we have the same denominator which is the bottom part of the fraction.

To do this we must find the least common multiple of the denominators.

The least common multiple is the smallest number that multiples of both of the denominators multiply to.

In this case the LCM is

We then multiply the numerator and denominator of by to get the same denominator because anything divided by itself is one so the fractions maintain their same value as the numbers change into the format we need to determine the answer.

To multiply a fraction you multiply the top number of the first fraction by the top number of the second fraction and the bottom number of the first fraction by the bottom number of the second fraction so it would look like this

After doing this we then subtract the first numerator (top part of the fraction) from the second numerator and place the result over the new denominator

The final answer is

4

Solve for .

Explanation

Subtract from both sides.

5

Solve for .

Explanation

To solve equations, you must perform the same operations on both sides.

Subtract 5 from both sides.

6

Solve for if

Explanation

To solve for we must get all of the numbers on the other side of the equation of .

To do this in a problem where a number is being added to , we must subtract the number from both sides of the equation.

In this case the number is so we subtract from each side of the equation to make it look like this

To subtract fractions we must first ensure that we have the same denominator which is the bottom part of the fraction.

To do this we must find the least common multiple of the denominators.

The least common multiple is the smallest number that multiples of both of the denominators multiply to.

In this case the LCM is

We then multiply the numerator and denominator of by to get the same denominator because anything divided by itself is one so the fractions maintain their same value as the numbers change into the format we need to determine the answer.

To multiply a fraction you multiply the top number of the first fraction by the top number of the second fraction and the bottom number of the first fraction by the bottom number of the second fraction so it would look like this

After doing this we then subtract the first numerator (top part of the fraction) from the second numerator and place the result over the new denominator

The final answer is

7

What is ?

Explanation

To get rid of a fraction, we multiply by the reciprocal. So we take and multiply both sides by :

and cancel each other out, so we are left with or .

8

Solve for .

Explanation

To solve for , the first thing we need to do is isolate the variable. That means we want ONLY on the left side of the equation.

Divide both sides by .

9

Solve for if .

Explanation

To solve for we must get all of the numbers on the other side of the equation as .

To do this in a problem where is being subtracted by a number, we must add the number to both sides of the equation.

In this case the number is so we add to each side of the equation to make it look like this

The s cancel on the left side and leave by itself.

Then we perform the necessary addition to get the answer of

The answer is .

10

Solve for .

Explanation

Subtract from both sides.

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