Sure, let's translate each of the phrases into an algebraic expression:
1. One-half x minus 12:
This means we'll start with x, take half of it, and then subtract 12. The corresponding algebraic expression is 0.5*x - 12.
2. X diminished by thrice y:
This means we start with x and subtract three times the value of y. The algebraic expression is x - 3*y.
3. Twice the sum of x and y:
Here, we are adding x and y together and then multiplying the result by 2. Our algebraic expression is 2*(x + y), which simplifies to 2*x + 2*y.
4. The sum of thrice x and y:
For this one, we are multiplying x by 3 and then adding the result to y. Therefore, the algebraic expression is 3*x + y.
5. 4 times x decreased by 5:
This implies we are multiplying x by 4 and then subtracting 5 from the result. The correct algebraic expression is 4*x - 5.
So, the algebraic expressions for these phrases are:
(0.5*x - 12, x - 3*y, 2*x + 2*y, 3*x + y, 4*x - 5)