Equations, Formulas, and the Problem-Solving Process2.12.1

1. Verify solutions to equations.2. Use formulas to solve problems.

Equation: Two expressions set equal.

Solution: A number that makes an equation true when it replaces the variable in the equation.

3x

537

What’s the difference?

Expression Equation

Simplified Solved

532

True False

53 x

solution. the is 2x

To Check a Possible SolutionReplace the variable in the equation with the value.If the resulting equation is true, the value is a solution.

SolutionsSolutions

Is a = 12 a solution?

5174 a

5174

517124

51748

5155

NO

Use parentheses!

SolutionsSolutions

Is a solution?56x 15238 xx

1556

2356

8

155

123

548

575

512

515

548

563

563

Yes

Determine which of the following is a solution for the equation.

a) –5

b) – 1

c) 2

d) 4

6 4 2 4 3 6 x x

2.1

Determine which of the following is a solution for the equation.

a) –5

b) – 1

c) 2

d) 4

6 4 2 4 3 6 x x

2.1

Formula:

The distance across a circle through its center.

An equation that describes a mathematical relationship.

Perimeter: The distance around a figure.

Area: The total number of square units that fill a figure.

Volume: The total number of cubic units that fill a space.

Circumference: The distance around a circle.

Radius: The distance from the center of a circle to any point on the circle.

Diameter:

FormulasFormulas See page 95!!!!

Area:

Perimeter:

lwA

wlP 22

Area: bhA21

Area:

Circumference:

2rA

rC 2dC

l

w

h

b

r

FormulasFormulas

Perimeter, Area or Volume?

Filling a pool with water? Volume

Cover for a pool? Area

Tile around a pool? Perimeter

Fencing? Perimeter

Laying carpet? Area

Putting up a wallpaper border?

Perimeter

FormulasFormulas

Suppose you have a rectangular pool that is 12 feet wide and 20 feet long. The pool has a constant depth of 4 feet. Find the perimeter, the area and the volume.

Perimeter: wlP 22

122202 P

2440 P

64P feet

FormulasFormulas

Suppose you have a rectangular pool that is 12 feet wide and 20 feet long. The pool has a constant depth of 4 feet. Find the perimeter, the area and the volume.

Area: lwA

1220A

240A square feet or ft2

FormulasFormulas

Suppose you have a rectangular pool that is 12 feet wide and 20 feet long. The pool has a constant depth of 4 feet. Find the perimeter, the area and the volume.

Volume:

cubic feet or ft3

lwhV

41220V

960V

A thermometer reads 30° C: what is this temperature in degrees Fahrenheit?

a) 34F

b) 49F

c) 86F

d) 112F

932

5 F C

2.1

A thermometer reads 30° C: what is this temperature in degrees Fahrenheit?

a) 34F

b) 49F

c) 86F

d) 112F

932

5 F C

2.1