Seven subtracted from five ties a number, and then the difference added to nine times a number.
a
15x^(-1)-3x
b
(2+x^3)/2
c
(5x-7)+9x
d
Linear
e
Nonlinear
c - (5x - 7) + 9x
To determine whether the expression "Seven subtracted from five ties a number, and then the difference added to nine times a number" is linear or nonlinear, we can analyze the given options.
a) 15x^(-1) - 3x: This expression contains a negative exponent and is therefore not linear.
b) (2 + x^3) / 2: This expression contains a cubic term (x^3) and is therefore not linear.
c) (5x - 7) + 9x: This expression contains only first-degree terms (x) and constants, and all variables are raised to the power of 1. Therefore, it is a linear expression.
d) Linear: This is not an expression but rather a description of the type of equation.
e) Nonlinear: This is not an expression but rather a description of the type of equation.
Based on the given options, the expression (5x - 7) + 9x is the only one that is linear.
To solve the problem, we need to translate the given sentence into an expression.
The given sentence says that "Seven subtracted from five ties a number, and then the difference added to nine times a number."
Let's break it down step by step:
1. "Seven subtracted from five" can be written as 5 - 7.
2. "Ties a number" means that the result of step 1 is equal to a variable, let's call it 'x'. So, we have 5 - 7 = x.
3. "The difference added to nine times a number" can be written as x + 9x.
Combining the above steps, the expression that represents the given sentence is (5 - 7) + (x + 9x).
Now, let's simplify this expression:
(5 - 7) + (x + 9x) = -2 + (10x) = 10x - 2
Therefore, the correct answer is b) (2+x^3)/2, which is represented by the expression 10x - 2.