one-half of a number is 8 less than two-thirds of the number.
write algebraic equation: the sum of x and 8 is 15
write algebraic equation: 4 more than x is 9
write algebraic equation: 5 less than twice x is equal to 35
write algebraic equation: the product of 10 and x is the same as -80
1. x/2 = 2x/3 - 8.
2. x + 8 = 15.
3. x + 4 = 9.
4. 2x-5 = 35.
5. 10x = -80.
To write the algebraic equations for the given statements, we need to translate the information provided into mathematical expressions. Let's go step by step:
1. "One-half of a number is 8 less than two-thirds of the number":
Let's represent the number with the variable 'x'. The equation can be written as:
(1/2)x = (2/3)x - 8
2. "The sum of x and 8 is 15":
The sum of x and 8 can be written as x + 8. The equation can be written as:
x + 8 = 15
3. "4 more than x is 9":
If we add 4 to x, it becomes 9. The equation can be written as:
x + 4 = 9
4. "5 less than twice x is equal to 35":
Twice x can be written as 2x. Subtracting 5 from twice x gives us 35. The equation can be written as:
2x - 5 = 35
5. "The product of 10 and x is the same as -80":
The product of 10 and x can be written as 10x. The equation can be written as:
10x = -80
These are the algebraic equations corresponding to each statement.