Write an equation using the information given in the problem. Use x as the variable. Then
solve the equation.
75.Three times a number is 17 more than twice the number. Find the number.
76.One added to three times a number is three less than four times the number. Find the
number.
77.If six times a number is subtracted from seven times the number, the result is. Find
the number.
78.If five times a number is added to three times the number, the result is the sum of seven
times the number and 9. Find the number.“Preview Exercises” are designed to reviewideas introduced earlier, as well as preview
ideas needed for the next section.- 9
92 CHAPTER 2 Linear Equations and Inequalities in One Variable
Simplify each expression.See Section 1.8.
- 6 a
t
69 a br
9- b
9
7
a-7
9
xb-
5
4
a-4
5
xb5
6
a6
5
b2
3
a3
2
bPREVIEW EXERCISES
OBJECTIVES OBJECTIVE 1 Use the multiplication property of equality.The addition
property of equality from Section 2.1is not enough to solve some equations, such as
Subtract 2 from each side.
Combine like terms.The coefficient of xis 3 , not 1 as desired. Another property, themultiplication
property of equality,is needed to change to an equation of the form
Since both 3xand 15 must represent the same number. Multiplying both 3x
and 15 by the same number will also result in an equality.
3 x= 15,
xa number.
3 x= 15
3 x= 15
3 x+ 2 - 2 = 17 - 2
3 x+ 2 = 17
3 x+ 2 = 17.
The Multiplication Property of Equality
2.2
1 Use the
multiplication
property of
equality.
2 Simplify, and
then use the
multiplication
property of
equality.Multiplication Property of EqualityIf A, B, and C represent real numbers, then the equations
and
are equivalent equations.
That is, we can multiply each side of an equation by the same nonzero number
without changing the solution.
AB ACBC
1 C Z 02
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