Question

Solve for x: 4(1 – x) + 2 x = -3( x + 1)

Answer 1

Answer:

4(1 – x) + 2 x = -3( x + 1)

first do 4 time 1= 4

then do 4 times x =4x

now the equation should look like this

4-4x+2x=-3(x+1)

then do the other side of the equation

-3(x+1)

=-3x-3

Now collect the like terms:

-4x-2x

now the equation should look like this

4-2x=-3x-3

now add 3x add on both sides

4-2x+3x=-3

put the 4 on the other side

-2x+3x=-3-4

now again collect the like terms (-2x+3x=1 which is just x and -3-4 =-7)

x=-7

answer

x=-7

Answer 2

Answer:

  $x=-7$                    PLEASE MARK ME AS BRAINLIEST

Step-by-step explanation:

$4(1-x)+2x=-3(x+1)$

Distribute 4 through the parentheses

$4-4x+2x=-3(x+1)$

Distribute -3 through the parentheses

$4-4x+2x=-3x-3$

Collect like terms

$-4x+2x$

Collect like terms by calculating the sum or difference of their coefficient

$(-4+2)x$

Calculate the sum

$-2x$

$4-2x=-3x-3$

Move variable to the left hand side and change its sign

$4-2x+3x=-3$

Why move an expression to the right?

We want to move an expression to the right to write the equation in a specific way.

The opposite needs to be added to both sides to preserve the relation between the sides. That is called the addition and subtraction property of equality/inequality

Step 1

Example

take the equation:

$x+a=b$

We want the expression a to be on the right hand side of the equation.

Step 1

example(cont)

To move the expression to the right -hand side, use the addition property , and add -a to both sides of the equation:

$x+a+(-a)=b+(-a)$

Simplify the left hand side and remove the parentheses on the right hand side:

$x+a+(-a)=b+(-a)\\x=b-a$

Now the expression a is on the right hand side :

$x=b-a$

Step 2:

Notice! when comparing  the beginning and the ending equation, it seems like we just moved the expression to the right hand side and changed its sign:

$x+a=b\\x=b-a$

This is a shorter way to use the same property.

Now came back to the original equation

$4-2x+3x=-3$

Move constant to to the right hand side and change its sign

$-2x+3x=-3-4$

collect like terms

$x=-3-4$

calculate the difference

$x=-7$

Why move a constant to the right?

We want to move a constant to the right because the mathematicians agreed upon a convention that the constants in the equation and inequalities always need to be on the right-hand side.

The opposite needs to be added to both sides to preserve the relation between the sides. That is called the addition and subtraction property of equality/inequality.

Step 1

example

Take the equation:

$x+3=5$

We want the constant 3to be on the right hand side of the equation.

Step 1

example (cont)

To move the constant to the right-hand side, use the addition property, and add -3 to both sides of the equation:

$x+3+(-3)=5+(-3)$

Simplify the left-hand side and remove the parentheses on the right - hand side:

$x+3+(-3)=5+(-3)\\x=5- 3$

Now , all the constants are on the right- hand side:

$x=5-3$

Step 2

Notice! when comparing the beginning and the ending equation, it seems like we just moved the constants to the right hand side and change its sign:

$x+3=5\\x=5-3$

This is a shorter way to use the same property.

PLEASE MARK ME AS BRAINLIEST