4
EXAMPLE
Use the Distributive Property
Solve the equation.
Student Help
a. 8x 2(x 7) 16
b. 5x 3(x 4) 28
STUDY TIP
Remember to distribute
the negative sign to
each term inside the
parentheses, not to
just the first term.
Solution
a. Distribute a negative number.
b. Distribute a positive number.
8x 2(x 7) 16
5x 3(x 4) 28
8x 2x 14 16
5x 3x 12 28
6x 14 16
8x 12 28
6x 14 14 16 14
8x 12 12 28 12
6x 30
8x 16
6x
30
6
6
8x
16
8
8
x5
x2
Use the Distributive Property and Combine Like Terms
Solve the equation. Check your solution in the original equation.
5. 6(x 2) 15
5
EXAMPLE
Student Help
STUDY TIP
In Example 5 you can
clear the equation of
fractions by multiplying
6. 8 4(x 1) 8
7. 3m 2(m 5) 10
Multiply by a Reciprocal First
2
3
Solve 4 (x 3).
Solution
2
by the reciprocal of .
3
2
3
4 (x 3)
3 (4) 3 冢23冣(x 3)
6x3
Write original equation.
3
2
Simplify.
63 x33
3x
Subtract 3 from each side.
Simplify both sides.
Multiply by a Reciprocal First
Solve the equation. Check your solution in the original equation.
3
8. 6 (x 7)
4
146
Chapter 3
Solving Linear Equations
2
3
Multiply each side by , the reciprocal of .
4
9. (x 2) 8
5
3
10. (x 1) 9
5