Given:
The algebra tiles of an equation.
To find:
The equation represented by the given model.
Solution:
On the left side of the model we have 4 tiles of (-x) and 3 tiles of (-1). So,
On the right side of the model we have 8 tiles of (-1). So,
Now, equate the LHS and RHS to get the equation.
Therefore, the equation for the given model is .
Answer:
False; they are equal.
Step-by-step explanation:
The equation is x + 20 > 4x - 1.
First, do the opposite of -1 and add one to the other side while -1+1 cancels out. Now it's x+21 > 4x. Now subtract x from both sides. Positive x minus negative x cancels out and 4x minus x or 1x is 3x. Now you're left with 21> 3x. Now do the inverse operation of multiplication and divide both sides by 3. Now the 3x over 3 cancels out and 21 divided by 3 is 7. So x is 7. If you substitute it in. It will be 7+20 which is 27 which is great than 4(7)-1 which is 28-1. 28-1 is 27. So, the equation is false. They are equal.
Answer:
Stephen weighs 80 lbs
Graham weighs 60 lbs
Step-by-step explanation:
Let Stephen the cat = S
Let Graham the cat = G
25% heavier = 125% = 125/100 = 1.25
50% heavier = 150% = 150/100 = 1.5
If both animals gained 20 lbs, S would be 25% heavier than G:
S + 20 = 1.25(G + 20)
⇒ S = 1.25(G + 20) - 20
⇒ S = 1.25G + 5
If both animals lost 20 lbs, S would be 50% heavier than G:
S - 20 = 1.5(G - 20)
⇒ S = 1.5(G - 20) + 20
⇒ S = 1.5G - 10
Equate both equations for S, and solve for G:
S = S
⇒ 1.25G + 5 = 1.5G - 10
⇒ -0.25G = -15
⇒ G = 60
Substitute found value for G into one of the equations for S and solve for S:
S = 1.5G - 10
⇒ S = 1.5 x 60 - 10
⇒ S = 90 - 10
⇒ S = 80
Stephen weighs 80 lbs
Graham weighs 60 lbs
