Answer:
1. y = -4
2. y = -0.73 (rounded; it's a repeating decimal and the 3 goes on. -0.7333333, and so on)
3. y = 24
4. c = -13.5
Step-by-step explanation:
30+7y=-2y-6
You want to get the y all by itself. So in order to do that you must combine the like terms from both sides. (so you'll combine the values with a variable, in this case y, and then you will combine the numbers without a variable.)
So, first, get the y's on the same side.
30+7y = -2y-6
Because 2 is negative "-2y", in order to cancel it out you have to ADD 2y to both sides.
30+(7y+2y)= -6
30+9y=-6
Remember, your goal is to get y by itself. So in order to do that, you have to get rid of the solo number on the same side, which is 30. Therefore, you must subtract 30 from BOTH SIDES.
9y= (-6 - 30)
Remember, when you're subtracting with negatives. The rule is: KEEP IT, SWITCH IT, SWITCH IT.
Keep the -6.
Switch the - to a +
And switch the positive thirty to a negative 30.
9y= -6 + (-30)
9y = -36
You want the y alone, so you have to cancel out the multiplication by its recipriocal (or opposite). The opposite of multiplication is division. So you must divide both sides by 9.
y= -36 ÷ 9
y= -4
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4(3y+4.1)=7.6
Use the distributive property and multiply the 4 (which is outside of the partenthesis) by what's inside of the parenthesis (3y+4.1).
4(3y+4.1):
4 x 3y = 12y
4 x 4.1 = 16.4
12y+16.4 = 7.6
Subtract 16.4 from both sides
12y = -8.8
Divide both sides by 12 to get the y by itself
y= -0.73 (repeating)
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3(y+1) = 4y-21
This is similar to the last problem. You must use the distributive property and multiply what's outside of the parenthesis by what's inside of the parenthesis.
3 x y = 3y
3 x 1 = 3
Rewrite the equation
3y+3 = 4y-21
Now this problem is similar to the very first problem
You need y by itself. So subtract 3y from both sides
3=(4y-3y)-21
3= 1y-21
Add 21 to both sides to get y by itself
24=1y
y=24
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3(2c+5) = 4(c-3)
This is just like the last two problems, you must use the distributive property.
3 x 2c = 6c
3 x 5 = 15
Rewrite equation.
6c+15 = 4(c-3)
Now you have to use the distrubtive property for 4(c-3)
4 x c = 4c
4 x (-3) = -12
Rewrite
6c + 15 = 4c - 12
Subtract both sides by 4c
(6c-4c) + 15 = -12
2c + 15 = -12
Subtract by 15 from both sides.
2c = -27
Divide both sides by 2, in order to get c by itself
c = -27 ÷ 2
c = -13.5
