# 3(x-4)=x+(-12)+2x -6x-2=-2(3x-1) 3(x-1)=4x+2 solve these and find out if these are one, none, or infinite

###### Question:

-6x-2=-2(3x-1)

3(x-1)=4x+2

solve these and find out if these are one, none, or infinite soulutions.

## Answers

6x-2<4x+12

move the variable and change its sign

6x-4x-12<12

move constant to right hand side and change its sign

6x-4x<12+2

Collect like term

2x<12+2

add the number

2x<14

divide both side

2< 14/2 or 14÷2

final answer :-

2<7

HOPE THIS HELPS

Step-by-step explanation:

First, you need to simplify step-by-step:

6x−24x+13

=6x+−24x+13

Now, you combine like terms:

=6x+−24x+13

=(6x+−24x)+(13)

=−18x+13

That's how you get your

=−18x+13

x < 7

hope this helps!

QUESTION 1

The given equation is

[tex]2.5(10 - x) + 10 = 72 - 1.5(5x + 12)[/tex]

Clear the decimal by multiplying through by 10 to get,

[tex]25(10 - x) + 100 = 720 - 15(5x + 12)[/tex]

Expand the bracket using the distributive property to get;

[tex]250 - 25x + 100 = 720 - 75x - 180[/tex]

Group similar terms to get,

[tex]- 25x + 75x = 720 - 250 - 100 - 180[/tex]

[tex]50x = 720 - 530[/tex]

[tex]50x = 190[/tex]

Divide through by 50 to get,

[tex]x = \frac{190}{50}[/tex]

[tex]x = \frac{19}{5}[/tex]

QUESTION 2

We want to solve the inequality,

[tex]16x \: \: 12(2x - 6) - 24[/tex]

We expand the bracket using the distributive property to obtain,

[tex]16x \: \: 24x - 72 - 24[/tex]

Group similar terms to get,

[tex]16x - 24x \: \: - 72 - 24[/tex]

Simplify to get,

[tex]- 8x \: \: - 96[/tex]

We divide both sides of the inequality by -8 and reverse the sign to obtain,

[tex]x \: < \: \frac{ - 96}{ - 8}[/tex]

[tex]x \: < \: 12[/tex]

QUESTION 3

Step 1.

Given:4(-6x – 3)+24x= -72x + 132

Step 2.

Distributive property:

-24x – 12 + 24x = -72x + 132

Step 3.

Combine like terms:

–12 = -72x + 132

Step 4.

Addition property of equality:

-144 = -72x

Step 5.

Division property of equality:

2=x

All the properties stated are correct.