Question

2.5 exercise
more practice, p. 804
guided practice
vocabulary check

1. copy and complete: addition and subtraction are operations.
2. which property of equality would you use to solve x - 5 = 7? explain.

skill check

1. solve the equation. check your solution.
2. x + 4 = 10
3. t + 9 = - 5
4. u - 3 = 6
5. y - 7 = - 2
6. 16 = a + 25
7. - 70 = b - 30
8. error analysis describe and correct the error in solving x + 8 = 10.
9. population from 1990 to 2000, the population of cresco, iowa, increased by 236. the population in 2000 was 3905. use an equation to find the population in 1990.

practice and problem solving

1. solve the equation. check your solution.
2. x + 7 = 12
3. y + 9 = 0
4. - 2 = z + 6
5. a - 5 = 8
6. b - 14 = - 3
7. 37 = c - 29
8. 21 + m = 4
9. n - 72 = 72
10. p - 24 = - 53
11. q + 8 = 57
12. r - 23 = - 6
13. 28 = g + 28
14. - 13 + t = 10
15. 216 = u - 129
16. 177 = 403 + w
17. rebate the advertised price of a dvd player is $185 after a $30 mail - in rebate. using the verbal model below, write and solve an equation to find the price of the dvd player before the rebate is applied.

price before rebate - rebate amount = price after rebate

1. biology when attacked by a giant hornet, japanese honeybees cluster together to form a ball around the hornet and then generate heat by buzzing. the honeybees can endure temperatures of up to 48°c, which is 3°c greater than the hornet can tolerate. find the maximum temperature tolerated by a japanese giant hornet.
2. archaeology the great pyramid in egypt was built around 2560 b.c. over the years, it has lost 30 feet of height off its top and is now 451 feet tall. find the original height of the great pyramid.

lesson 2.5 solving equations using addition or subtraction

Explanation:

Step1: Solve equation 3 ($x + 4=10$)

Subtract 4 from both sides. $x+4 - 4=10 - 4$

Step2: Simplify

$x = 6$

Step3: Solve equation 4 ($t + 9=-5$)

Subtract 9 from both sides. $t+9 - 9=-5 - 9$

Step4: Simplify

$t=-14$

Step5: Solve equation 5 ($u - 3=6$)

Add 3 to both sides. $u-3 + 3=6 + 3$

Step6: Simplify

$u = 9$

Step7: Solve equation 6 ($y - 7=-2$)

Add 7 to both sides. $y-7 + 7=-2 + 7$

Step8: Simplify

$y = 5$

Step9: Solve equation 7 ($16=a + 25$)

Subtract 25 from both sides. $16-25=a + 25-25$

Step10: Simplify

$a=-9$

Step11: Solve equation 8 ($-70=b - 30$)

Add 30 to both sides. $-70 + 30=b-30 + 30$

Step12: Simplify

$b=-40$

Step13: Solve equation 9 (Error analysis)

The error is adding 8 to the right - hand side instead of subtracting 8. Correctly, for $x + 8=10$, subtract 8 from both sides: $x+8 - 8=10 - 8$, so $x = 2$

Step14: Solve equation 10 (Population problem)

Let $p$ be the population in 1990. The equation is $p + 236=3905$. Subtract 236 from both sides: $p+236-236=3905 - 236$, so $p = 3669$

Step15: Solve equation 11 ($x + 7=12$)

Subtract 7 from both sides. $x+7 - 7=12 - 7$, so $x = 5$

Step16: Solve equation 12 ($y + 9=0$)

Subtract 9 from both sides. $y+9 - 9=0 - 9$, so $y=-9$

Step17: Solve equation 13 ($-2=z + 6$)

Subtract 6 from both sides. $-2-6=z + 6-6$, so $z=-8$

Step18: Solve equation 14 ($a - 5=8$)

Add 5 to both sides. $a-5 + 5=8 + 5$, so $a = 13$

Step19: Solve equation 15 ($b - 14=-3$)

Add 14 to both sides. $b-14 + 14=-3 + 14$, so $b = 11$

Step20: Solve equation 16 ($37=c - 29$)

Add 29 to both sides. $37+29=c - 29+29$, so $c = 66$

Step21: Solve equation 17 ($21 + m=4$)

Subtract 21 from both sides. $21 + m-21=4 - 21$, so $m=-17$

Step22: Solve equation 18 ($n - 72=72$)

Add 72 to both sides. $n-72 + 72=72 + 72$, so $n = 144$

Step23: Solve equation 19 ($p - 24=-53$)

Add 24 to both sides. $p-24 + 24=-53 + 24$, so $p=-29$

Step24: Solve equation 20 ($q + 8=57$)

Subtract 8 from both sides. $q+8 - 8=57 - 8$, so $q = 49$

Step25: Solve equation 21 ($r - 23=-6$)

Add 23 to both sides. $r-23 + 23=-6 + 23$, so $r = 17$

Step26: Solve equation 22 ($28=g + 28$)

Subtract 28 from both sides. $28-28=g + 28-28$, so $g = 0$

Step27: Solve equation 23 ($-13 + t=10$)

Add 13 to both sides. $-13 + t+13=10 + 13$, so $t = 23$

Step28: Solve equation 24 ($216=u - 129$)

Add 129 to both sides. $216+129=u - 129+129$, so $u = 345$

Step29: Solve equation 25 ($177 = 403+w$)

Subtract 403 from both sides. $177-403=403 + w-403$, so $w=-226$

Step30: Solve equation 26 (Rebate problem)

Let $x$ be the price before rebate. The equation is $x-30 = 185$. Add 30 to both sides: $x-30 + 30=185 + 30$, so $x = 215$

Step31: Solve equation 27 (Biology problem)

Let $h$ be the maximum temperature the hornet can tolerate. The equation is $h+3 = 48$. Subtract 3 from both sides: $h+3 - 3=48 - 3$, so $h = 45^{\circ}C$

Step32: Solve equation 28 (Archaeology problem)

Let $h$ be the original height. The equation is $h-30 = 451$. Add 30 to both sides: $h-30 + 30=451 + 30$, so $h = 481$ feet

Answer:

Solutions for equations 3 - 28 are: $x = 6,t=-14,u = 9,y = 5,a=-9,b=-40,x = 2,p = 3669,x = 5,y=-9,z=-8,a = 13,b = 11,c = 66,m=-17,n = 144,p=-29,q = 49,r = 17,g = 0,t = 23,u = 345,w=-226,x = 215,h = 45^{\circ}C,h = 481$ feet respectively.