Sure! Let's solve the given question step-by-step.
We start with the equation:
[tex]\[ \frac{5(x + 15)}{3} = 2(x - 5) \cdot 17 \][/tex]
Step 1: Eliminate the fraction.
The left-hand side of the equation has a fraction. To eliminate the fraction, we can multiply both sides of the equation by 3:
[tex]\[ 5(x + 15) = 2(x - 5) \cdot 51 \][/tex]
Step 2: Simplify both sides of the equation.
Now, we simplify each side of the equation separately.
For the left-hand side:
[tex]\[ 5(x + 15) = 5x + 75 \][/tex]
For the right-hand side, first simplify inside the parentheses, and then multiply:
[tex]\[ 2(x - 5) \cdot 51 = 2(51x - 255) = 34x - 170 \][/tex]
So now the equation becomes:
[tex]\[ 5x + 75 = 34x - 170 \][/tex]
Step 3: Solve for \( x \).
To isolate \( x \), first move all terms involving \( x \) to one side and constant terms to the other side. We'll do this by subtracting \( 5x \) from both sides and adding \( 170 \) to both sides:
[tex]\[ 75 + 170 = 34x - 5x \][/tex]
[tex]\[ 245 = 29x \][/tex]
Step 4: Divide both sides by 29 to solve for \( x \).
[tex]\[ x = \frac{245}{29} \][/tex]
So, the solution to the equation is:
[tex]\[ x = \frac{245}{29} \][/tex]
Summary:
- After multiplying both sides by 3 and simplifying each side, we get the equation \( 5x + 75 = 34x - 170 \).
- Solving for \( x \) results in \( x = \frac{245}{29} \).
This [tex]\( x \)[/tex] value is the solution to the original equation.
