Answer:

1.x + 4

2.b + 7

3.0.5x or x/2

4.3(x + 10) or 3x + 30

5.mn4 or 4mn

Step-by-step explanation:

1.x increased by 4:

To translate this phrase into an algebraic expression, we first need to recognize that "increased by" means addition. So, "x increased by 4" can be written as x + 4. This expression means that we're taking some value x, and then adding 4 to it.

2.b more than 7:

Similar to the first expression, "more than" implies addition. So, "b more than 7" can be written as b + 7. This expression means that we're taking some value b, and then adding 7 to it.

3.half of x:

This expression is a little trickier, but it means exactly what it says: we're taking half of the value x. Mathematically, this can be written as 0.5x or x/2. Both of these expressions mean the same thing: we're taking x and dividing it by 2.

4.thrice the sum of a number x and 10:

"Thrice" means three times, and "the sum of" implies addition. So, "thrice the sum of a number x and 10" can be written as 3(x + 10) or 3x + 30. Both of these expressions mean the same thing: we're taking some value x, adding 10 to it, and then multiplying the result by 3.

5.the product of m and n *+4xt4 mtn:

This expression is a bit unclear, but it seems to be asking for the product of m and n, multiplied by 4. This can be written as 4mn, where the order of the variables doesn't matter (multiplication is commutative).