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# Literal Equations and Formulas

Sep 17, 2022

## Key Concepts

• Rewrite literal equations
• Use literal equations to solve problems
• Rewrite a formula
• Apply formulas

## Literal equation

An equation that states the relationship between two or more quantities using variables is called a literal equation.

Example: Frame a literal equation for the perimeter of a rectangle.

The perimeter of a rectangle = Sum of all sides

= Length + Width + Length + Width

Let P be the perimeter, l be the length and w be the width of the rectangle

P = 2 × (l+ w)

### Formula

An equation that states the relationship between one quantity and one or more quantities is called a formula

We use formulas for finding the unknown values like perimeter and area.

1. Formula for perimeter of square

P = 4 × Side

2. Formula for perimeter of rectangle

P = 2 (length + width)

3. Formula for area of square

A = Side × Side

4. Formula for area of rectangle

A = length × width

### Rewriting literal equations

Use properties of equality to solve literal equations for a variable just as you do linear equations.

Example:

If the side of the square is s, then perimeter P = s + s + s + s

P = 4 × s

If we are given the perimeter of a square, to find the length of each side, we need to divide the formula of perimeter of a square by “4”.

P/4 = 4×s/4

⇒ s = P/4

### Rewriting a formula

We can rewrite a formula to find the unknown values. Then we get the value of one quantity in terms of another quantity.

Example: Write the formula for calculating the length of a rectangle if the perimeter and the width are given.

Sol: The formula for the perimeter of a rectangular farm is   P = 2(l+ w)

P = 2l+ 2w

P – 2w = 2l + 2w – 2w

P – 2w/2 = 2l/2

l= P−2w/2

∴ The perimeter formula in terms of l is l = P−2w/2

### Apply formula

We can use the formulas to rewrite/reframe them and solve problems.

Example: The high temperature on a given winter day is 25° C. What is the temperature in °F?

Rewrite the formula to find the Fahrenheit temperature that is equal to 25° C

C = 5/9(F – 32)

9/5 . C = 9/5 . 5/9(F – 32)

9/5C = F – 32

9/5C + 32 = F – 32 + 32

9/5C + 32 = F

Use the formula to find the Fahrenheit temperature equivalent to 25° C

9/5C + 32 = F

9/5(25) + 32 = F

45 + 32 = F

F = 77°

## Exercise

• Solve 5x-4 = 4x
• The triangle shown is isosceles. Find the length of the third side of the triangle.
• Solve the equation – 3(8+3h) = 5h+4
• Find the missing value in – 2(2x- ?) + 1 = 17-4x
• Is the equation – 4(3-2x) = -12-8x an identity?

So, the high temperature on a given winter day is 77° F.

### Concept Map

If an equation has pronumerals on both sides, collect the like terms to one side by adding or subtracting terms.

Example: 4x + 7 = 2(2x + 1) + 5

4x + 7 = 4x + 2 + 5

4x + 7 = 4x + 7

7 = 7

### What have we learned

• If an equation has pronumerals on both sides, collect the like terms to one side by adding or subtracting terms

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