To set up the expression “one sixth x 5 one fifth x 2” as a system of equations, we first need to break down the components of the expression into manageable parts. The phrase seems to combine fractional coefficients with a variable, which we will denote as x.
1. The expression begins with one sixth, which can be written as the fraction 1/6.
2. It then includes x, suggesting that we will multiply this fraction by x, resulting in (1/6)x.
3. Next, we have 5, indicating that we’ll set this up as part of the equation structure later.
4. The second half of the expression contains one fifth, expressed as 1/5, followed by x and 2. Therefore, this part corresponds to (1/5)x, which again we can use with the 2 later to structure our equation.
Based on these components, we could set up two separate equations to represent these relationships:
- Equation 1: (1/6)x = 5 – This equation states that one sixth of x is equal to 5.
- Equation 2: (1/5)x = 2 – This indicates that one fifth of x is equal to 2.
Thus, we have established a system of equations:
- 1) (1/6)x = 5
- 2) (1/5)x = 2
These equations can now be solved simultaneously to find the value of x.