6th Grade Math Textbook, Progress

128 Chapter 4

Equations and Inequalities

4-4

Write as an equation. Then label each equation as openor closed.

If the equation is closed, write whether it is trueor false.

1. A number divided by 3.85 is equal 2. Six less than three times ten is equal
   to one. to twenty.


2. Two more than twice a number is three. 4. Half of eight is three less than seven.

Determine if the given value of the variable is the solution

of the equation. Write yesor no.

5. 9 x
   8 35, when x 3 6. 19  2 p6, when p 7


6. 3 k
   4.9 8.5, when k12.3 8. 18 (8 m) 17, when m 7

Leslie and Clark each write a word sentence as an equation.

An equation is a statement that shows that two mathematical expressions are equal.

Leslie’s equation is:

Twice nine decreased by three is fifteen.

2 • 9  3  15

Leslie’s equation is a closed

sentence because it contains no

variables. A closed sentence is

either true or false.

To determine whether an

equation is true or false:


Simplify each side of the

equation using the order of

operations.


Compare the sides to

determine if they make a

true statement.

2 • 9  3  15

18  3 

?

15

15  15 true

The equation, 2  9  3 15, is a

truestatement.

Clark’s equation is:

Five times a number n, minus two equals eight.

5 n  2  8

Clark’s equation is an open sentence

because it contains a variable. An open

sentence is neither true nor false.

To determine whether a value is a

solution of an equation:


Replace the variable with the given

value.


Simplify using the order of operations

and determine the value of the variable

that makes a true statement.

5 n 2 8, when n3 and n 2

5( 3 )  2  8 and 5( 2 )  2  8

15  2 

?

8 and 10  2 

?

8

13  8 false and 8  8 true

2 is the solutionof the equation.

It makes a truestatement.

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