Which expressions could complete this equation so that it has one solution? 4(4x - 3) - 6x
*There are two answers*
12x - 12 -2x **
9x - 12
4x + 2(3x - 6)
4(2x + 3) - 24 **
Marie has $830 in her bank account and withdraws $60 each month. Denise has $970 in her bank account and withdraws $80 each month.
In how many months will Marie and Denise have equal amounts of money in their accounts?
4 **
5
7
9
the first is not an equation, no equals sign. So I have no idea what it wants.
marie=830-60m
Denise=970-80m
set them equal, and solve for m
830-60m=970-80m
140=20m
m= you are wrong.
To solve the first equation, we can start by simplifying the expression:
4(4x - 3) - 6x
First, distribute 4 to each term inside the parentheses:
16x - 12 - 6x
Next, combine the like terms:
(16x - 6x) - 12
10x - 12
Now, if we want the equation to have only one solution, we need to set it equal to a specific value. In this case, we want the equation to equal 0 since that means there is only one solution.
10x - 12 = 0
To solve for x, add 12 to both sides:
10x = 12
Then, divide both sides by 10:
x = 12/10
Simplifying the fraction:
x = 6/5
So, one possible expression that completes the equation and has one solution is:
12x - 12 - 2x
Substituting x = 6/5:
12(6/5) - 12 - 2(6/5)
= 72/5 - 60/5 - 12/5
= (72 - 60 - 12)/5
= 0/5
= 0
Another possible expression is:
4(2x + 3) - 24
Similarly, substituting x = 6/5:
4(2(6/5) + 3) - 24
= 4(12/5 + 3) - 24
= 4(12/5 + 15/5) - 24
= 4(27/5) - 24
= 108/5 - 120/5
= (108 - 120)/5
= (-12)/5
= -12/5
For the second question:
To find in how many months Marie and Denise will have equal amounts of money in their accounts, we can create an equation based on the given information.
Let x represent the number of months.
For Marie, the amount remaining in her account after x months is given by:
830 - 60x
For Denise, the amount remaining in her account after x months is given by:
970 - 80x
To find when both amounts are equal, we set them equal to each other and solve for x:
830 - 60x = 970 - 80x
Add 80x to both sides:
80x - 60x = 970 - 830
Simplify:
20x = 140
Divide both sides by 20:
x = 7
Therefore, it will take 7 months for Marie and Denise to have equal amounts of money in their accounts.