100 CHAPTER 2 Linear Equations and Inequalities in One Variable
Step 2 Subtract 3z.
Combine like terms.
Add 3.
Combine like terms.Step 3 Divide by 3.
Step 4 Check that E^43 Fis the solution set. NOW TRY
z=
4
3
3 z
3
=
4
3
3 z= 4
3 z- 3 + 3 = 1 + 3
3 z- 3 = 1
6 z- 3 - 3 z= 3 z+ 1 - 3 z
CAUTION In an expression such as in Example 4,the sign
acts like a factor of and affects the sign of everyterm within the parentheses.
Change to -in bothterms.= 8 z- 3 - 2 z
= 8 z+ 1 - 1213 + 2 z 2
= 8 z- 113 + 2 z 2
8 z- 13 + 2 z 2
- 1
8 z - 13 + 2 z 2 -
NOW TRY
EXERCISE 5
Solve.
24 - 417 - 2 t 2 = 41 t- 12Using the Four Steps to Solve an EquationSolve
Step 1
Distributive property
Combine like terms.Step 2 Add 8x.
Combine like terms.
Subtract 16.
Combine like terms.Step 3 Divide by
Step 4 CHECK Original equation
Let
Multiply and add.
Subtract and multiply.✓ True
Since the solution 0 checks, the solution set is 506. NOW TRY
16 = 16
4142 32 - 16
414 - 02 32 - 8122
434 - 31024 32 - 810 + 22 x=0.
414 - 3 x 2 = 32 - 81 x+ 22
x= 0
- 4.
- 4 x
- 4
=
0
- 4
- 4 x= 0
16 - 4 x- 16 = 16 - 16
16 - 4 x= 16
16 - 12 x+ 8 x= 16 - 8 x+ 8 x
16 - 12 x= 16 - 8 x
16 - 12 x= 32 - 8 x- 16
414 - 3 x 2 = 32 - 81 x+ 22
414 - 3 x 2 = 32 - 81 x+ 22.
EXAMPLE 5
Be careful
with signs.OBJECTIVE 2 Solve equations with fractions or decimals as coefficients.
To avoid messy computations, we clear an equation of fractions by multiplying each
side by the least common denominator (LCD) of all the fractions in the equation.
NOW TRY ANSWERS
4.E^53 F 5. 506
NOW TRY
EXERCISE 4
Solve.
5 x- 1 x+ 92 =x- 4http://www.ebook777.com
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