I got a Math Test tomorrow and i can't stand about this Equations!! Can you Help Me?

Question

The Test is about Linear Equations or/and Quadratic Equations!
But by now i just can solve this ones:
7x+15=12x+5
or/and
300=100+4x

But I can't do this ones:

a. -3x+5=2x-10
b. 14-3x=1.5+5
c. 3+5(x+2)=7x-1
d. x^2+4.5x=0
e.-x^2+10x=0

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Can you please, explain to me how to solve it step by step?
Thank You so much for help me and got a good notes (maybe..) tomorrow is my test, one of the things is that i dont get nervous but with this x.x I love Math but sometimes i can't stand some hard problem like tahta x.x

Thanks & Bye!

Answer 1

a) -3x+5=2x-10
=>-3x-2x=-10-5
=>-5x= -15
=>x=-15/-5=3 ans
b)14-3x=1.5+5
=>-3x=1.5+5-14
=>-3x=6.5-14= -7.5
=>x=-7.5/-3=2.5
c)3+5(x+2)=7x-1
=>3+5x+10=7x-1
=>5x-7x= -1-3-10
=> -2x= -14
=>x=-14/-2=7
d)x^2+4.5x=0
=>x(x+4.5)=0
As the product of two numbers cannot be zero unless one of them is zero,therefore,either x=0 or x+4.5=0
Therefore,x=0 or -4.5
e)x^2+10x=0
=>x(x+10)=0
As the product of two numbers cannot be zero until and unless one of them is zero,hence either x=0 or x+10=0
Therefore,x=0 or x= -10

Answer 2

a. -3x+5=2x-10
5x=15
x=3

b. 14-3x=1.5+5
3x=7.5
x=2.5

c. 3+5(x+2)=7x-1
3 + 5x+10=7x-1
-2x=-14
x=7

d. x^2 +4.5x=0
x(x+4.5)=0
X=0, X=-4.5

e. X^2+10X=0
-X(x+10)=0
x=0, x=10

Answer 3

a. add 3x to each side
5=5x -10
Add 10 to each side
15=5x
Divide both sides by 5
3 = x

b. I am guessing you typed this one wrong, and it should be:
14 - 3x = 1.5x +5
Add 3x to each side
14 = 4.5x + 5
Subtract 5 from each side
9 = 4.5x
Divide by 4.5
2=x

c. Multiply 5 by both x and 2
3 +5x + 10 = 7x - 1
Subtract 5x from both sides and combine 3 and 10
13 = 2x -1
Add 1 to both sides
14 = 2x
Divide by 2
7 = x

d. Divide by x
x(x+4.5) = 0
Either x = 0 or x+4.5=0
subtract 4.5 from both sides
Either x = 0 or x = -4.5

e Divide by negative x
-x(x-10) = 0
-x = 0 (you can drop neg) or x - 10 =0
Add 10 to both
x=0 or x = 10


Maru is correct if you copied b right. On e, she missed the - sign in front. And dramione copied c wrong.

Answer 4

a. add 3x to the other side and add the 10 to the other side. It is then 5x=15. Then just divide by 5 and get x=3.

b. add 3x to the other side and subtract the 6.5(1.5+5.5) to the other side as well. Divide by 3 and get 7.5 over 5. because you cant have a decimal or a fraction inside another fraction, you multiply 7.5 over 5 by 2 which is 15 over 10. Reduce it to 3 over 2.

c. Distribute the 5(x+2). You get 5x +10. The problem then becomes 5x+13=7x-1. Add teh 1 to the other side and subtract the 5x. You get 2x=14. Divide by 2 and you get x=7.

Use the quadratic formula for d and e, which can be found at the source below. I hope I helped.

Answer 5

1)7x+15=12x+5, 12x-7x = 15-5 =10 =5x, then x=2
2)300 =100 + 4x, 4x=300-100=200, then x=200/4 50
a) -3x +5 =2x-10, 2x+3x= 5x = 5 +10 =15, then x=15/5 =3
b) 14-3x=1.5 +5, 3x = 14 -6.5 = 7.5, x=7.5/3 =2.5
c) 3+5(x+2) = 7x-1, 3 + 5x +10 = 7x-1, 7x-5x= 2x =
13+1= 14 , x= 14/2 = 7
d) x*2 +4.5x=0 ,x*2= -4.5x, x= -4.5
e)-x*2+10x = 0, x*2=10x, x=10

Answer 6

a. -3x+5=2x-10
add 10 to each side
-3x+15=2x
add 3x to each side
15=5x
divide by 5
x=3
b. 14-3x=1.5+5
multiply everything by 2
28-6x=3+10
simplify
28-6x=13
subtract 28
-6x=-15
divide by -6
x=15/6
simplify
x=5/2
c. 3+5(x+5)=7x-1
distribute the 5
3+5x+25=7x-1
simplify right side
5x+28=7x-1
add 1 to both sides
subtract 5x from both sides
29=2x
divide by 2
x=29/2
d. x^2+4.5x=0
factor out an x
x(x+4.5)=0
set 0 equal to both parts
0=x 0=x+4.5
subtract 4.5
x=-4.5; x=0
e. -x^2+10x)=0
factor out a negative x
-x(x-10)=0
set 0 equal to both parts
0=-x 0=x-10
divide right by -1; add 10 to both sides in left
x=0; x=10

Answer 7

a)
5 = 5x - 10
5x = 15
x = 3
b)
14 - 3x = 1.5x + 5 is the question?
9 = 4.5 x
x = 2
c)
13 + 5x + 10 = 7x - 1
23 = 2x - 1
2x = 24
x = 12
d)
x.(x + 4.5) = 0
x = 0 , x = - 4.5
e)
x² - 10x = 0
x.(x - 10) = 0
x = 0, x = 10
Good luck with test!

Answer 8

For ones with x factors on both sides, you have to get all the terms on one side and then solve for x. For ones with x squared, you can use the quadratic formula. You would use the quadratic formula on d and e and just simple manipulation on a, b, and c.