Let's solve the equation [tex]\( 8(5x - 9) + 6(7 + x) = 430 \)[/tex] step-by-step.
### Step 1: Distribute the Constants
Distribute the 8 and the 6 through their respective parentheses.
[tex]\[ 8(5x - 9) + 6(7 + x) = 430 \][/tex]
This becomes:
[tex]\[ 8 \cdot 5x - 8 \cdot 9 + 6 \cdot 7 + 6 \cdot x = 430 \][/tex]
Simplifying each term, we get:
[tex]\[ 40x - 72 + 42 + 6x = 430 \][/tex]
### Step 2: Combine Like Terms
Now, combine the terms involving [tex]\( x \)[/tex] and the constant terms on the left side of the equation.
[tex]\[ (40x + 6x) + (-72 + 42) = 430 \][/tex]
This simplifies to:
[tex]\[ 46x - 30 = 430 \][/tex]
### Step 3: Isolate the Variable Term
To isolate the term with [tex]\( x \)[/tex], add 30 to both sides of the equation:
[tex]\[ 46x - 30 + 30 = 430 + 30 \][/tex]
This simplifies to:
[tex]\[ 46x = 460 \][/tex]
### Step 4: Solve for [tex]\( x \)[/tex]
Finally, divide both sides by 46 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{460}{46} \][/tex]
Simplifying the fraction, we get:
[tex]\[ x = 10 \][/tex]
So, the solution to the equation [tex]\( 8(5x - 9) + 6(7 + x) = 430 \)[/tex] is:
[tex]\[ x = 10.0 \][/tex]
