Question

leveled practice in 11 - 20, write equivalent expressions. 11. 3(m + 3) = 3m+9 12. 20n - 4m = 4( n - m) 13. 3(x - 6) 14. -2x + 10 15. 8(2y + 1/4) 16. 5.7+(3z + 0.3) 17. 5w - 15 18. 2x + 4y 19. -52(y - 2) 20. 3/4·(z³·4)

Explanation:

Step1: Apply distributive property for 11

$3(m + 3)=3\times m+3\times3 = 3m + 9$

Step2: Factor out 4 for 12

$20n-4m = 4\times5n-4\times1m=4(5n - 1m)$

Step3: Apply distributive property for 13

$3(x - 6)=3\times x-3\times6=3x-18$

Step4: Factor out - 2 for 14

$-2x + 10=-2\times x+(-2)\times(-5)=-2(x - 5)$

Step5: Apply distributive property for 15

$8(2y+\frac{1}{4})=8\times2y+8\times\frac{1}{4}=16y + 2$

Step6: Rearrange terms for 16

$5.7+(3z + 0.3)=(5.7+0.3)+3z=6 + 3z$

Step7: Factor out 5 for 17

$5w-15=5\times w-5\times3=5(w - 3)$

Step8: Factor out 2 for 18

$2x + 4y=2\times x+2\times2y=2(x + 2y)$

Step9: Simplify the inner - bracket first then outer for 19

$-5[2(y - 2)]=-5\times(2y-2\times2)=-5\times(2y - 4)=-5\times2y-(-5)\times4=-10y + 20$

Step10: Apply associative property for 20

$\frac{3}{4}\cdot(z^{3}\cdot4)=(\frac{3}{4}\cdot4)\cdot z^{3}=3z^{3}$

Answer:

1. $3m + 9$
2. $4(5n - 1m)$
3. $3x-18$
4. $-2(x - 5)$
5. $16y + 2$
6. $6 + 3z$
7. $5(w - 3)$
8. $2(x + 2y)$
9. $-10y + 20$
10. $3z^{3}$