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].
### 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].
