Final answer:
A number decreased by 34 is the same as 38 minus 5 times the number. The equation representing this relationship is x - 34 = 38 - 5x. By solving this equation, we find that the unknown number is 12.
Step-by-step explanation:
We have a mathematical expression representing a number decreased by 34 that is equal to 38 minus 5 times the number. First, we will let the variable x represent the unknown number. The relationship described can be written as an equation: x - 34 = 38 - 5x.
To solve the equation, we first add 5x to both sides to get all x terms on one side and constants on the other, resulting in 6x - 34 = 38. Next, we add 34 to both sides, giving us 6x = 72. Finally, dividing both sides by 6 gives us x = 12. Therefore, the unknown number is 12.
It is also helpful to apply an understanding of substitution to check the solution. By substituting x with 12 into the original equation, we will verify if both sides of the equation are equal.
Substituting 12 into the equation results in 12 - 34, which equals -22, and on the other side, 38 - 5(12) also equals -22. Both sides are indeed equal, confirming that the solution x = 12 is correct.