PRE-ALGEBRA

PRE-ALGEBRA

Lesson 2-4 Warm-Up

PRE-ALGEBRA

Variables and Equations (2-4)

equation – a number sentence with an “equal” signExamples: 9 + 2 = 11 a numerical expression equal to a numerical

expressionx + 7 = 37 or 37 = x + 7 an algebraic expression equal to a numerical

expression (or vice versa)a + (-3) = 2a + 5 an algebraic expression equal to an an algebraic

expressiontrue equation – an equation in which both sides equal one another Example: 6 + 12 = 18false equation – an equation in which both sides don’t equal one another Example: 6 ≠ 3 + 4open sentence – an equation with one or more variables

Example: Write the equation “nine times the opposite of five is forty-five.” State whether the equation is true, false or an open sentence.   Words nine times the opposite of five is forty-five 9 x (-5) = 45

The equation is false, because 9 x (-5) = -45, and -45 ≠ 45

What is an “equation”?

What is a “true equation”, “false equation”, and “open sentence”?

PRE-ALGEBRA

State whether each equation is true, false, or

an open sentence. Explain.

a. 3(b – 8) = 12

c. –9 + 5 = – 4

b. 7 – (–6) = 1

open sentence, because there is a variable

=/ false, because 13 1

true, because – 4 = – 4

Variables and EquationsLESSON 2-4

Additional Examples

PRE-ALGEBRA

Write an equation for Six times a number added to the

number is the opposite of forty-two. State whether the equation

is true, false, or an open sentence. Explain.

The equation is an open sentence, because there is a variable.

Equation 6x + =x –42

six times the numberWords

6x

added to

added to x is

isthe oppositeof forty-two

–42

thenumber

Variables and EquationsLESSON 2-4

Additional Examples

PRE-ALGEBRA

Variables and Equations (2-4)

solution of an equation – the value of the variable (what the variable is equal to) to make the equation true

To check the solution to an equation, substitute to see if the variable makes the equation true.

Example: On a mule ride, a rider and his gear weighs 185 pounds (lb.) If the gear weighs 20 pounds, does the rider weigh 160 pounds? Words weight of rider plus weight of gear is 185 pounds Define Let w = weight of rider Equation w + 20 = 185

160 + 20 = 185 Substitute or replace 160 for “w” to check). 180 ≠ 185 Simplify.No, the rider cannot weigh 160 pounds. Example: Can you stack eight books that are 3 in. thick inside a box that is 18 in. tall? 8 x 3 = 24 24 in. ≠ 18 in. Add up 3 in. eight times.

No, you cannot stack all of the books inside the box.

What is a “solution to an equation”?

How do you check the solution to an equation?

PRE-ALGEBRA

Is 45 a solution of the equation 120 + x = 75?

120 + x = 75

No, 45 is not a solution of the equation.

120 + 45 75 Substitute 45 for x.

165 75=/

Variables and EquationsLESSON 2-4

Additional Examples

PRE-ALGEBRA

A gift pack must hold 20 lb of food. Apples weigh 9 lb

and cheese weighs 5 lb. Can the jar of jam that completes the

package weigh 7 lb?

9 + 5 + j = 20

Equation 5 + =j 20

weight of cheese

Words plus

= weight of jam.

is 20 lbweight of

jam

9

j

weight of apples plus

Let

+

14 + j = 20 Add.

14 + 7 20 Substitute 7 for the variable.

No, the jar of jam cannot weigh 7 lb.

21 20 =/

Variables and EquationsLESSON 2-4

Additional Examples

PRE-ALGEBRA

1. Is b + 3b – 1 = 15 true, false, or an open sentence?

2. Write an equation for A number added to seven times the number is the opposite of thirty-two. Is the equation true, false, or an open sentence?

3. Is 25 a solution of the equation 175 – x = 150?

4. Can you stack eight books that are each 3 in. thick inside a box that is 18 in. tall?

yes

open sentence

7x + x = –32; open sentence

no

Lesson Quiz

Variables and EquationsLESSON 2-4