# Common Core: High School - Algebra : Rearrange Formulas and Solve Equations: CCSS.Math.Content.HSA-CED.A.4

## Example Questions

### Example Question #1 : Rearrange Formulas And Solve Equations: Ccss.Math.Content.Hsa Ced.A.4

To calculate the slope of a line, the following formula is used.

Solve this equation for .

Explanation:

This question is asking to rearrange the slope formula to highlight a quantity of interest, specifically

To rearrange the formula, perform algebraic operations. Recall that whatever operation that is done to one side needs to also be done on the other side in order to keep the equation balanced.

First, multiply both sides by the quantity  in order to move it from the right side of the equation to the left side. Performing the opposite operation allows for rearranging to occur.

Next, add  to both sides of the equation.

Therefore, the equation solved for  is

### Example Question #2 : Rearrange Formulas And Solve Equations: Ccss.Math.Content.Hsa Ced.A.4

To calculate the slope of a line, the following formula is used.

Solve this equation for .

Explanation:

This question is asking to rearrange the slope formula to highlight a quantity of interest, specifically

To rearrange the formula, perform algebraic operations. Recall that whatever operation that is done to one side needs to also be done on the other side in order to keep the equation balanced.

First, multiply both sides by the quantity  in order to move it from the right side of the equation to the left side. Performing the opposite operation allows for rearranging to occur.

Next, subtract  to both sides of the equation.

Now, divide by negative one on both sides.

Therefore, the equation solved for  is,

### Example Question #3 : Rearrange Formulas And Solve Equations: Ccss.Math.Content.Hsa Ced.A.4

To calculate the slope of a line, the following formula is used.

Solve this equation for

Explanation:

This question is asking to rearrange the slope formula to highlight a quantity of interest, specifically

To rearrange the formula, perform algebraic operations. Recall that whatever operation that is done to one side needs to also be done on the other side in order to keep the equation balanced.

First, multiply both sides by the quantity  in order to move it from the right side of the equation to the left side. Performing the opposite operation allows for rearranging to occur.

Next divide by  on both sides.

### Example Question #3 : Rearrange Formulas And Solve Equations: Ccss.Math.Content.Hsa Ced.A.4

To calculate the slope of a line, the following formula is used.

Solve this equation for .

Explanation:

This question is asking to rearrange the slope formula to highlight a quantity of interest, specifically

To rearrange the formula, perform algebraic operations. Recall that whatever operation that is done to one side needs to also be done on the other side in order to keep the equation balanced.

First, multiply both sides by the quantity  in order to move it from the right side of the equation to the left side. Performing the opposite operation allows for rearranging to occur.

Next divide by  on both sides.

Now subtract  from both sides.

Finally, divide by negative one.

### Example Question #5 : Rearrange Formulas And Solve Equations: Ccss.Math.Content.Hsa Ced.A.4

The equation for a circle centered at (0,0) is,

Solve the equation for .

Explanation:

This question is asking to rearrange this formula to highlight a quantity of interest, specifically

To rearrange the formula, perform algebraic operations. Recall that whatever operation that is done to one side needs to also be done on the other side in order to keep the equation balanced.

To isolate  take the square root of each side.

Therefore, the equation solved for  is

### Example Question #4 : Rearrange Formulas And Solve Equations: Ccss.Math.Content.Hsa Ced.A.4

The equation for a circle centered at (0,0) is,

Solve the equation for .

Explanation:

This question is asking to rearrange this formula to highlight a quantity of interest, specifically

To rearrange the formula, perform algebraic operations. Recall that whatever operation that is done to one side needs to also be done on the other side in order to keep the equation balanced.

To isolate  subtract  from both sides and then take the square root.

Therefore, the equation solved for  is

### Example Question #5 : Rearrange Formulas And Solve Equations: Ccss.Math.Content.Hsa Ced.A.4

The equation for a circle centered at (0,0) is,

Solve the equation for .

Explanation:

This question is asking to rearrange this formula to highlight a quantity of interest, specifically

To rearrange the formula, perform algebraic operations. Recall that whatever operation that is done to one side needs to also be done on the other side in order to keep the equation balanced.

To isolate  subtract  from both sides and then take the square root.

Therefore, the equation solved for  is

### Example Question #6 : Rearrange Formulas And Solve Equations: Ccss.Math.Content.Hsa Ced.A.4

To calculate simple interest the following formula is used.

Solve the equation for .

Explanation:

This question is asking to rearrange this formula to highlight a quantity of interest, specifically

To rearrange the formula, perform algebraic operations. Recall that whatever operation that is done to one side needs to also be done on the other side in order to keep the equation balanced.

Since  is being multiplied by , divide by  on both sides.

Therefore, the equation solved for  is,

### Example Question #7 : Rearrange Formulas And Solve Equations: Ccss.Math.Content.Hsa Ced.A.4

To calculate simple interest the following formula is used.

Solve the equation for .

Explanation:

This question is asking to rearrange this formula to highlight a quantity of interest, specifically

To rearrange the formula, perform algebraic operations. Recall that whatever operation that is done to one side needs to also be done on the other side in order to keep the equation balanced.

Since  is being multiplied by , divide by  on both sides.

Therefore, the equation solved for  is,

### Example Question #10 : Rearrange Formulas And Solve Equations: Ccss.Math.Content.Hsa Ced.A.4

To calculate simple interest the following formula is used.

Solve the equation for .