45 mins
Step-by-step explanation:
The correct answers are:
#1) B - 2x+9
#2) B - 16
#3) D - x+10y
#4) C - 8(3p+8)
#5) No equation, cannot be done
#6) B - w = -4
#7) A - q = 4
#8) D - q = 144
#9) A - b = 8
#10) A - y = -125
#11) D - a = 6
#12) B - x = 3
#13) C - x = 24
#14) D - -4
#15) D - Z>13
#16) same as 15
#17) Not listed; Q < -22
#18) C - y < -3
#19) A - K>-20
#20) D - g< 7
#21) A - V > 8
Explanation:
#1) "Nine more than" means something plus 9. "Two times a number" means 2x. Together, this gives us 2x+9.
#2) For 3m-5 if m=7, substitute 7 for m. 3(7)-5 = 21-5 = 16.
#3) To simplify 4x+8y-3x+2y, combine like terms. We can use the commutative property to rewrite the like terms together: 4x-3x+8y+2y. Combining like terms, we have x+10y.
#4) To factor, we pull out the GCF. To find the GCF, we find the prime factorization of 24 and 64:
24 = 2(12) = 2(4)(3) = 2(2)(2)(3)
64 = 2(32) = 2(4)(8) = 2(2)(2)(2)(4) = 2(2)(2)(2)(2)(2)
They have 3 2's in common, so the GCF is 2(2)(2) = 8. Pulling this out of our expression, we have:
24p+64 = 8(3p+8)
#5) We have no equation to solve.
#6) We add 8 to each side:
w-8+8 = -12+8; w = -4
#7) We divide both sides by 3:
3q/3 = 12/3; q = 4
#8) We multiply both sides by 6:
(q/6)(6) = 24(6); q = 144
#9) 3b-9 = 15
First, add 9 to each side:
3b-9+9 = 15+9; 3b = 24
Now divide both sides by 3:
3b/3 = 24/3; b = 8
#10) y/5 + 10 = -15
First subtract 10 from both sides:
y/5+10-10 = -15-10; y/5 = -25
Now multiply both sides by 5:
(y/5)(5) = -25(5); y = -125
#11) -3(4-a) = 6
First use the distributive property:
-3(4) - -3(a) = 6; -12+3a = 6
Add 12 to each side:
-12+3a+12 = 6+12; 3a = 18
Divide both sides by 3:
3a/3 = 18/3; a = 6
#12) 5(x+6) = 45
Use the distributive property:
5(x)+5(6) = 45; 5x+30=45
Subtract 30 from each side:
5x+30-30 = 45-30; 5x=15
Divide both sides by 5:
5x/5 = 15/5; x = 3
#13) 4x+8=104
Subtract 8 from each side:
4x+8-8 = 104-8; 4x=96
Divide both sides by 4:
4x/4 = 96/4; x = 24
#14) We want a number larger than -6. For negative numbers, this means a number closer to 0; the number closest to 0 is -4.
#15) Add 4 to each side: z-4+4 > 9+4; z > 13
#16) Same as 15
#17) Subtract 7 from each side: q+7-7<-15-7; q<-22
#18) Divide both sides by -3 (remember, when you multiply or divide an inequality by a negative number, you must flip the inequality symbol): -3y/-3>9/-3; y<-3
#19) Multiply both sides by 5: (k/5)(5)>-4(5); k>-20
#20) 4g-8<20
First add 8 to each side: 4g-8+8<20+8; 4g<28
Divide both sides by 4: 4g/4<28/4; g<7
#21) v/-2 +12 < 8
First subtract 12 from each side: (v/-2)+12-12<8-12; (v/-2)<-4
Multiply both sides by -2 (remember to flip the inequality symbol): (v/-2)(-2)<-4(-2); v>8