Chapter 9 - XYZ Custom Plus
Chapter 9 - XYZ Custom Plus
Chapter 9 - XYZ Custom Plus
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
9.3 The Multiplication Property of Equality<br />
533<br />
ExAmplE 4<br />
Solve for x: 2 }x<br />
4 x 5 } 8 5 15<br />
4. Solve for x: 2} }}<br />
3 4 } x 5 }6 }}<br />
5 }<br />
SOlutiOn The reciprocal of 2 }}<br />
4 5 } is 2 }5 }}<br />
4 }.<br />
2 4 } 5<br />
x 5 8 } 15<br />
− 5 — 4 1 2 4 } 5<br />
x 2<br />
5 − 5 — 4 1 8 } 15 2<br />
x 5 2 2 } 3<br />
Many times, it is convenient to divide both sides by a nonzero number to solve<br />
an equation, as the next example shows.<br />
ExAmplE 5<br />
SOlutiOn<br />
Solve for x: : 4x<br />
5 220<br />
If we divide both sides by 4, the left side will be just x, which is what<br />
we want. It is okay to divide both sides by 4 because division by 4 is equivalent to<br />
multiplication by }}<br />
1 4 } , and the multiplication property of equality states that we can<br />
multiply both sides by any number so long as it isn’t 0.<br />
4x<br />
5 220<br />
4x<br />
} 5 } 220 Divide both sides by 4<br />
4 4<br />
x 5 25<br />
Division<br />
Because 4x<br />
x means “4 times x,” the factors in the numerator of 4x<br />
x }}<br />
} are 4 and x.<br />
4<br />
Because the factor 4 is common to the numerator and the denominator, we divide<br />
it out to get just x.<br />
ExAmplE 6<br />
SOlutiOn<br />
Solve for x: 23x<br />
3 1 7 5 25<br />
We begin by adding 27 to both sides to reduce the left side to 23x<br />
3 .<br />
23x<br />
3 1 7 5 25<br />
23x<br />
3 1 7 1 (−7) 5 25 1 (−7) Add 27 to both sides<br />
23x<br />
3 5 212 Addition<br />
23x<br />
3<br />
} 5 } 212 Divide both sides by 23<br />
−3 −3<br />
5. Solve for x: : 6x<br />
5 242<br />
Note<br />
If we multiply each<br />
side by }}<br />
1 4 } , the solution<br />
looks like this:<br />
− 1 4 (4x<br />
) 5 −1<br />
4 (220)<br />
1 }1 }}<br />
4 } ? 4 2 x 5 25<br />
1x 5 25<br />
x 5 25<br />
6. Solve for x: 25x<br />
5 1 6 5 214<br />
x 5 4<br />
Division<br />
With more complicated equations we simplify each side separately before applying<br />
the addition or multiplication properties of equality. The examples below<br />
illustrate.<br />
ExAmplE 7<br />
SOlutiOn<br />
usual.<br />
Solve for x: : 5x<br />
2 8x<br />
1 3 5 4 2 10<br />
We combine similar terms to simplify each side and then solve as<br />
5x<br />
2 8x<br />
1 3 5 4 2 10<br />
23x<br />
3 1 3 5 26 Simplify each side<br />
23x<br />
3 1 3 1 (−3) 5 26 1 (−3) Add 23 to both sides<br />
23x<br />
3 5 29 Addition<br />
23x<br />
3<br />
} 5 } 29<br />
Divide both sides by 23<br />
−3 −3<br />
x 5 3<br />
Division<br />
7. Solve for x: : 3x<br />
2 7x<br />
1 5 5 3 2 18<br />
Answers<br />
4. 2 }}<br />
8 5 } 5. 27 6. 4 7. 5
Change language