Step 4 Use the multiplication property of equality to isolate xon the left.
Divide by 4.Step 5 Check by substituting 4 for xin the original equation.
CHECK Original equation
Let
Simplify.10 = 10 ✓ True
21 - 12 + 12 10
214 - 52 + 3142 4 + 6 x=4.
21 x- 52 + 3 x=x+ 6
x= 4
4 x
4
=
16
4
SECTION 2.1 Linear Equations in One Variable 51
Eliminate the fractions.
Multiply each side by the LCD, 6.The solution checks, so the solution set is 5 - 16. NOW TRY
NOW TRY
EXERCISE 3
Solve.
51 x- 42 - 9 = 3 - 21 x+ 162
Alwayscheck
your work.The solution checks, so is the solution set. NOW TRY
OBJECTIVE 5 Solve linear equations with fractions or decimals.When
fractions or decimals appear as coefficients in equations, our work can be made eas-
ier if we multiply each side of the equation by the least common denominator (LCD)
of all the fractions. This is an application of the multiplication property of equality.
Solving a Linear Equation with FractionsSolve
Step 1
Step 2 Distributive property
Multiply.
Distributive property
Multiply.
Combine like terms.Step 3 Add 17.
Combine like terms.Step 4 Divide by 7.
Step 5 CHECK
LetAdd and subtract in the
numerators.Simplify each fraction.- 4 =- 4 ✓ True
1 - 5 - 4
6
6
+
- 10
2
- 4
x=-1.
- 1 + 7
6
+
21 - 12 - 8
2
- 4
x+ 7
6
+
2 x- 8
2
=- 4
x=- 1
7 x
7
=
- 7
7
7 x=- 7
7 x- 17 + 17 =- 24 + 17
7 x- 17 =- 24
x+ 7 + 6 x- 24 =- 24
x+ 7 + 312 x 2 + 31 - 82 =- 24
x+ 7 + 312 x- 82 =- 24
6 a
x+ 7
6
b + 6 a
2 x- 8
2
b = 61 - 42
6 a
x+ 7
6
+
2 x- 8
2
b = 61 - 42
x+ 76 +
2 x- 82 =-4.
EXAMPLE 4
546
NOW TRY
EXERCISE 4
Solve.
x- 4
4+
2 x+ 4
8= 5
NOW TRY ANSWERS
- 506 4. 5116