Literal Equations2.5

Objective

To rewrite and use literal equations & formulas.

Objective

Essential Understanding…

We will use the methods we’ve learned in this chapter to isolate any particular variable.

Essential Understanding…

Literal Equation (page 109)

Term:

Literal Equation

Equation that involves two or more variables.

Term:

One thing I would do…

One thing I would do…When creating an equation from a real world situation, I would use the first letter of each object as the variable;

One thing I would do…When creating an equation from a real world situation, I would use the first letter of each object as the variable; that way, it might be easier for you to remember what each variable represents.

What is different about these…

They contain more than 1 variable.

What is different about these…

They contain more than 1 variable. You will not get a final number answer;

What is different about these…

They contain more than 1 variable. You will not get a final numerical answer; instead your goal is to isolate the variable

What is different about these…

They contain more than 1 variable. You will not get a final number answer; instead your goal is to isolate the variable◦Alone on either side of the equation.

What is different about these…

Keep your textbooks on page 109

10x + 5y = 80

Keep your textbooks on page 109

10x + 5y = 80

Keep your textbooks on page 109

Coefficients represent the cost of each item, while the constant on the right represents the total cost or the total amount of money you have.

Your turn…

Got it on the top of page 110 (a)

Your turn…

Got it on the top of page 110 (a)◦4 = 2m – 5n for m 4 + 5n = 2m = m

Your turn…

Got it on the top of page 110 (a)◦ = m

Values: n = -2 m = -3n = 0 m = 2n = 2 m = 7

Your turn…

Choices in life:

When doing the evaluating part of equations, you can either:

Choices in life:

When doing the evaluating part of equations, you can either:

(a) Use literal equation solving to isolate the variable; then, plug in the value given and evaluate.

Choices in life:

When doing the evaluating part of equations, you can either:

(a) Use literal equation solving to isolate the variable; then, plug in the value given and evaluate.

OR

Choices in life:

When doing the evaluating part of equations, you can either:

(b) Plug in the value right away and solve.

Choices in life:

When doing the evaluating part of equations, you can either:

(b) Plug in the value right away and solve.

I’ll show you what I mean with part B.

Choices in life:

10x + 5y = 80

Literal

10x + 5y = 80

Literal

5y = 80 – 10xy = 16 – 2x

x = 3 y = 16 – 6 =

10

10x + 5y = 80

Literal

5y = 80 – 10xy = 16 – 2x

x = 6 y = 16 – 12 = 4

10x + 5y = 80

Literal

5y = 80 – 10xy = 16 – 2x

x = 6 y = 16 – 12 = 4

Solving Equations

10x + 5y = 80

Literal

5y = 80 – 10xy = 16 – 2x

x = 6 y = 16 – 12 = 4

Solving Equations

10x + 5y = 80

10x + 5y = 80

Literal

5y = 80 – 10xy = 16 – 2x

x = 6 y = 16 – 12 = 4

Solving Equations

10x + 5y = 80

x = 3

10x + 5y = 80

Literal

5y = 80 – 10xy = 16 – 2x

x = 6 y = 16 – 12 = 4

Solving Equations

10x + 5y = 80

x = 330 + 5y = 80

10x + 5y = 80

Literal

5y = 80 – 10xy = 16 – 2x

x = 6 y = 16 – 12 = 4

Solving Equations

10x + 5y = 80

x = 330 + 5y = 80

5y = 50y = 10

10x + 5y = 80

Literal

5y = 80 – 10xy = 16 – 2x

x = 6 y = 16 – 12 = 4

Solving Equations

10x + 5y = 80

x = 660 + 5y = 80

5y = 20y = 4

10x + 5y = 80

Formulas:

P 110Formulas:

P 110

No need to memorize (at leastthis year)

Formulas:

P 110

No need to memorize (at leastthis year) but you do need to solve for the variable asked for.

Formulas:

P = 2l + 2w for wExample:

P = 2l + 2w for wNeed to get w isolated

P = 2l + 2w for w

Subtract 2l from both sides

Need to get w isolated

P = 2l + 2w for wP – 2l = 2w

Subtract 2l from both sides

Need to get w isolated

P = 2l + 2w for wP – 2l = 2w

Subtract 2l from both sides

Divide both sides by w’s coefficient

P = 2l + 2w for wP – 2l = 2w

Hint: when you divide by a coefficient, put the entireexpression over it.

Divide both sides by w’s coefficient

P = 2l + 2w for wP – 2l = 2w

Hint: when you divide by a coefficient, put the entireexpression over it.

Divide both sides by w’s coefficient

Other hints:

You can multiply or divide by multiple terms simultaneously.

Other hints:

You can multiply or divide by multiple terms simultaneously.

C = 2r for r

Other hints:

You can multiply or divide by multiple terms simultaneously.

for r

Other hints:

You can multiply or divide by multiple terms simultaneously.

for r

Other hints:

When you divide an expression involving addition or subtraction by a coefficient, put parentheses around the expression and put it over the coefficient you divided by.

Other hints:

S = for hOther hints:

S = for hOther hints:

S = for h

We want to isolate the h, so we subtract the other term 1st.

Other hints:

S = for h- -

We want to isolate the h, so we subtract the other term 1st.

Other hints:

S = for h- -

S - =

We want to isolate the h, so we subtract the other term 1st.

Other hints:

S = for h

S - =

Since h has 3 coefficients, we can divide by all 3 at once.

Other hints:

S = for h

Leaving us with h on the right hand side alone.

Other hints:

S = for h

Leaving us with h on the right hand side alone.

Other hints: