Let's solve the equation step-by-step:
Given equation:
[tex]\[ 6(x + 5) = 3(2x + 10) \][/tex]
1. Distribute the numbers outside the parentheses on both sides of the equation:
- Left side: \( 6(x + 5) \)
[tex]\[ \Rightarrow 6x + 30 \][/tex]
- Right side: \( 3(2x + 10) \)
[tex]\[ \Rightarrow 6x + 30 \][/tex]
So, the equation becomes:
[tex]\[ 6x + 30 = 6x + 30 \][/tex]
2. Simplify the equation:
- Subtract \( 6x \) from both sides of the equation:
[tex]\[ 6x + 30 - 6x = 6x + 30 - 6x \][/tex]
[tex]\[ 30 = 30 \][/tex]
3. Interpret the simplified form:
- After simplifying, we end up with the equation \( 30 = 30 \), which is a true statement and holds no matter what value \( x \) takes.
This means that there are no specific values for \( x \) that make this equation true because it's always true for any value of \( x \).
Therefore, the solution to the equation is:
[tex]\[ \text{All real numbers} \][/tex]
