Answer: 1) -1/10 2) s-3w/2 3)5x+8−x=6x−2(x−4) 4) x<-1 5)
x<4 6) 2x+12 7) 15x-30 8) 24-10x
9) 8+x² = 5(x - 2) 10) 315minutes
Step-by-step explanation:
1) 4=10x+5
Solving the equation, 10x = 4-5
10x = -1
x= -1/10
2) s=3w+2x
Solving for x is like making x the subject of the formula
s-3w = 2x
Dividing both sides by 2
x = s-3w/2
3) Out of the option, the equation 5x+8−x=6x−2(x−4) is equal
Opening the bracket at the right hand side of the equation, we have,
6x-2x+8
= 4x+8...1
Similarity left hand side gives
5x-x+8
=4x+8.. 2
Which shows that eqn 1 and 2 are identity.
4)4x – 5 + x < –10
Solving this inequality
5x-5<-10
5x<-10+5
5x<-5
x<-1
5) 30 – 4x > 6x – 10
Solving this
-4x-6x>-10-30
-10x>-40
Multiplying both sides by minus will change the sign to have
10x<40
x<4
6) if 8x + 3y...(1), and y = 4 – 2x
Substituting y=4-2x into (1), we have
8x + 3(4-2x)
=8x + 12 - 6x
= 2x+12
7) If 3x + 6y, when y = 2x – 5
We have 3x + 6(2x-5)
3x + 12x - 30
= 15x-30
8) If 2x – 4y, when y = 3x – 6
Equivalent expression will be
2x - 4(3x-6)
= 2x - 12x +24
-10x + 24
= 24-10x
9) Eight increased by the square of a number, is five times the difference of the number and two."
This statement is represented by
Let the unknown number be 'x'
The square of the number is x²
If eight is increased by x², it become 8+x²...(1)
.The difference between the unknown number and two gives x - 2...(2)
Therefore, eight increased by the square of a number, is five times the difference of the number and two." becomes 8+x² = 5(x - 2)
10) If it takes 15minutes to cook 1pound of turkey, it will take (21×15) minutes to cook 21pounds of the same turkey i.e 315minutes
