Solve for [tex][tex]$x$[/tex][/tex].

[tex]\[ 5(x-10) = 30 - 15x \][/tex]

A. [tex][tex]$x=1$[/tex][/tex]

B. [tex][tex]$x=4$[/tex][/tex]

C. [tex][tex]$x=5$[/tex][/tex]

D. [tex][tex]$x=8$[/tex][/tex]



Answer :

To solve the equation [tex]\( 5(x - 10) = 30 - 15x \)[/tex] for [tex]\( x \)[/tex], follow these steps:

### 1. Simplify both sides of the equation:

First, distribute the [tex]\( 5 \)[/tex] on the left-hand side:
[tex]\[ 5(x - 10) = 5x - 50 \][/tex]

So, the equation becomes:
[tex]\[ 5x - 50 = 30 - 15x \][/tex]

### 2. Move all terms involving [tex]\( x \)[/tex] to one side of the equation:

Add [tex]\( 15x \)[/tex] to both sides to collect the [tex]\( x \)[/tex] terms on the left:
[tex]\[ 5x + 15x - 50 = 30 \][/tex]

Which simplifies to:
[tex]\[ 20x - 50 = 30 \][/tex]

### 3. Isolate the term with [tex]\( x \)[/tex]:

Add 50 to both sides to move the constant term to the right:
[tex]\[ 20x - 50 + 50 = 30 + 50 \][/tex]

This simplifies to:
[tex]\[ 20x = 80 \][/tex]

### 4. Solve for [tex]\( x \)[/tex]:

Divide both sides by 20 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{80}{20} \][/tex]

which simplifies to:
[tex]\[ x = 4 \][/tex]

### Conclusion:

The solution to the equation [tex]\( 5(x - 10) = 30 - 15x \)[/tex] is [tex]\( x = 4 \)[/tex]. Among the given options, the correct answer is [tex]\( x = 4 \)[/tex].