Final answer:
The solution to the equation -4(5x - 7) = -18 is found by distributing the -4, moving the constants to one side, and isolating the variable x. Simplifying the terms, we get x = 2.3.
Step-by-step explanation:
To solve the equation -4(5x - 7) = -18, we need to perform the following steps:
- Distribute the -4 into the parentheses: -4 × 5x = -20x and -4 × -7 = +28, so the equation becomes -20x + 28 = -18.
- Next, subtract 28 from both sides to isolate the term with the variable: -20x + 28 - 28 = -18 - 28, simplifying to -20x = -46.
- Finally, divide both sides by -20 to solve for x: -20x / -20 = -46 / -20, which simplifies to x = 46/20. This fraction can be reduced to x = 23/10 or x = 2.3.
In conclusion, the solution to the equation is x = 2.3.
Always eliminate terms wherever possible to simplify the algebra and check the answer to see if it is reasonable.