90 CHAPTER 2 Linear Equations and Inequalities in One Variable
NOW TRY
EXERCISE 7
Solve.
413 x- 22 - 111 x- 42 = 3CHECK Original equation
Let
Multiply.✓ True
The check results in a true statement, so the solution set is. NOW TRY
Using the Distributive Property When SolvingSolve
Distributive property
Multiply.
Combine like terms.
Subtract 5 from each side.
Combine like terms.Check by substituting 1 for xin the original equation. The solution set is.
NOW TRY516
x= 1
x+ 5 - 5 = 6 - 5
x+ 5 = 6
6 + 15 x- 1 - 14 x= 6
3122 + 315 x 2 - 1112 - 1114 x 2 = 6
3 12 + 5 x 2 - 111 + 14 x 2 = 6 - 11 + 14 x 2 =- 111 + 14 x 2
312 + 5 x 2 - 11 + 14 x 2 = 6
312 + 5 x 2 - 11 + 14 x 2 = 6.
EXAMPLE 7
5176
58 = 58
51 - 12 + 17 + 2 5 + 51 + 2
31172 - 12 + 17 + 2 5 + 31172 + 2 t=17.
3 t- 12 + t+ 2 = 5 + 3 t+ 2
Be sure to
distribute to all
terms within the
parentheses. Be careful here!CAUTION Be careful to apply the distributive property correctlyin a problem
NOW TRY ANSWERS like that in Example 7,or a sign error may result.
- 556 7. 576
Complete solution available
on the Video Resources on DVD
2.1 EXERCISES
1.Concept Check Decide whether each of the following is an expressionor an equation.
If it is an expression, simplify it. If it is an equation, solve it.
(a) (b)
(c) (d)
2.Concept Check Which pairs of equations are equivalent equations?
A. and B. and
C. and D. and
3.Concept Check Which of the following are notlinear equations in one variable?
A. B. C. D.
4.Explain how to check a solution of an equation.Solve each equation, and check your solution. See Examples 1–5.
- 8.x- 18 = 22 9.x- 6 =- 9 10.x- 5 =- 7
x- 3 = 9 x- 9 = 8 x- 12 = 19x^2 - 5 x+ 6 = 0 x^3 =x 3 x- 4 = 0 7 x- 6 x= 3 + 9 xx+ 3 = 9 x= 6 4 +x= 8 x=- 4x+ 2 = 6 x= 4 10 - x= 5 x=- 55 x+ 8 - 4 x= 7 - 6 y+ 12 + 7 y=- 55 x+ 8 - 4 x+ 7 - 6 y+ 12 + 7 y- 5NOW TRY
EXERCISE 6
Solve.
= 4 - 8 x- 95 x- 10 - 12 xhttp://www.ebook777.com
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