Example
Solve:
0.8x−5=7
Solution:
The only decimal in the equation is
0.8. Since
0.8=108, the LCD is
10. We can multiply both sides by
10 to clear the decimal.
| 0.8x−5=7 |
Multiply both sides by the LCD. | 10(0.8x−5)=10(7) |
Distribute. | 10(0.8x)−10(5)=10(7) |
Multiply, and notice, no more decimals! | 8x−50=70 |
Add 50 to get all constants to the right. | 8x−50+50=70+50 |
Simplify. | 8x=120 |
Divide both sides by 8. | 88x=8120 |
Simplify. | x=15 |
Check: Let x=15. | |
0.8(15)−5=?712−5=?7
7=7✓
| |
Example
Solve:
0.06x+0.02=0.25x−1.5
Answer:
Solution:
Look at the decimals and think of the equivalent fractions.
0.06=1006,0.02=1002,0.25=10025,1.5=1105
Notice, the LCD is 100.
By multiplying by the LCD we will clear the decimals.
| 0.06x+0.02=0.25x−1.5 |
Multiply both sides by 100. | 100(0.06x+0.02)=100(0.25x−1.5) |
Distribute. | 100(0.06x)+100(0.02)=100(0.25x)−100(1.5) |
Multiply, and now no more decimals. | 6x+2=25x−150 |
Collect the variables to the right. | 6x−6x+2=25x−6x−150 |
Simplify. | 2=19x−150 |
Collect the constants to the left. | 2+150=19x−150+150 |
Simplify. | 152=19x |
Divide by 19. | 19152=1919x |
Simplify. | 8=x |
Check: Let x=8. | |
0.06(8)+0.02=0.25(8)−1.50.48+0.02=2.00−1.5
0.50=0.50✓
| |