Final answer:
The given algebraic equation is solved by distributing the constants, combining like terms, and isolating the variable h to find that h = 1.5.
Step-by-step explanation:
To solve the algebraic equation 3(2h + 7) = 4(9 – h), we begin by distributing the constants 3 and 4 across the parentheses. This simplifies the equation to 6h + 21 = 36 – 4h. Next, we combine like terms by adding 4h to both sides and subtracting 21 from both sides to isolate the variable h. The equation now becomes 10h = 15. Dividing both sides by 10 gives us the value of h, which is h = 1.5.