Beginning Algebra, 11th Edition

66. 67. 68.

69. 70.

71.Concept Check Write an equation that requires the use of the multiplication property

of equality, where each side must be multiplied by and the solution is a negative number.

72.Concept Check Write an equation that requires the use of the multiplication property

of equality, where each side must be divided by 100 and the solution is not an integer.

Write an equation using the information given in the problem. Use x as the variable. Then

solve the equation.

73.When a number is multiplied by 4, the result is 6. Find the number.

74.When a number is multiplied by 4, the result is 10. Find the number.

75.When a number is divided by , the result is 2. Find the number.

76.If twice a number is divided by 5, the result is 4. Find the number.

Simplify each expression.See Section 1.8.

Solve each equation.See Section 2.1.

81. 4 x+ 5 + 2 x= 7 x 82. 2 x+ 5 x- 3 x+ 4 = 3 x+ 2

41 - 5 + 2 p 2 - 31 p- 42 214 k- 72 - 41 - k+ 32

• 13 m+ 52 - 41 - 1 + 6 x 2

PREVIEW EXERCISES

- 5

-

2

3

2

5

x+

1

10

x-

1

20

x= 18

1

3

x-

1

4

x+

1

12

x= 3

• 5 x+ 4 x- 8 x= 0 8 w- 4 w+w=- 3 9 x- 3 x+x=- 4

SECTION 2.3 More on Solving Linear Equations 97

OBJECTIVES

More on Solving Linear Equations

2.3

1 Learn and use the
four steps for
solving a linear
equation.

2 Solve equations
with fractions or
decimals as
coefficients.

3 Solve equations
with no solution or
infinitely many
solutions.

4 Write expressions
for two related
unknown quantities.

OBJECTIVE 1 Learn and use the four steps for solving a linear equation.

We now apply bothproperties of equality to solve linear equations.

Solving a Linear Equation

Step 1 Simplify each side separately.Clear (eliminate) parentheses, frac-

tions, and decimals, using the distributive property as needed, and

combine like terms.

Step 2 Isolate the variable term on one side.Use the addition property if

necessary so that the variable term is on one side of the equation

and a number is on the other.

Step 3 Isolate the variable.Use the multiplication property if necessary to

get the equation in the form a number, or a number (Other

letters may be used for variables.)

Step 4 Check.Substitute the proposed solution into the originalequation

to see if a true statement results. If not, rework the problem.

x= =x.