Final answer:
The linear equation is solved by distributing the number outside the parentheses, combining like terms, and then isolating the variable x. The final answer is x = 1/4.
Step-by-step explanation:
To solve the linear equation 3(−4x + 5) = 12, let's follow the standard steps for solving a linear equation.
Distribute the 3 to both terms inside the parentheses: 3 × (−4x) + 3 × 5 = 12, which simplifies to −12x + 15 = 12.
Subtract 15 from both sides of the equation to get the x term by itself: −12x + 15 − 15 = 12 − 15, which simplifies to −12x = −3.
Finally, divide both sides of the equation by −12 to solve for x: −12x / −12 = −3 / −12, which simplifies to x = 1/4.
By following these steps, we've found that the value that satisfies the equation is x = 1/4.