Answer :
- Set up the equation: $\frac{5}{6} x - 4 + T = \frac{1}{2} x - 4$.
- Isolate $T$: $T = (\frac{1}{2} x - 4) - (\frac{5}{6} x - 4)$.
- Simplify the expression: $T = \frac{1}{2} x - 4 - \frac{5}{6} x + 4$.
- Combine like terms and simplify: $T = -\frac{1}{3} x$.
$\boxed{-\frac{1}{3} x}$
### Explanation
1. Understanding the Problem
We are given the expression $\frac{5}{6} x-4$ and we want to find a term, let's call it $T$, that when added to this expression, results in $\frac{1}{2} x-4$. This can be written as an equation:$$\frac{5}{6} x - 4 + T = \frac{1}{2} x - 4$$
2. Isolating the Unknown Term
To find $T$, we need to isolate it on one side of the equation. We can do this by subtracting $\frac{5}{6} x - 4$ from both sides:$$T = (\frac{1}{2} x - 4) - (\frac{5}{6} x - 4)$$
3. Simplifying the Expression
Now, let's simplify the expression for $T$ by distributing the negative sign and combining like terms:$$T = \frac{1}{2} x - 4 - \frac{5}{6} x + 4$$$$T = (\frac{1}{2} x - \frac{5}{6} x) + (-4 + 4)$$
4. Combining Like Terms
To combine the $x$ terms, we need a common denominator. The least common denominator for 2 and 6 is 6. So, we rewrite $\frac{1}{2} x$ as $\frac{3}{6} x$:$$T = (\frac{3}{6} x - \frac{5}{6} x) + 0$$$$T = -\frac{2}{6} x$$
5. Final Simplification
Finally, we simplify the fraction:$$T = -\frac{1}{3} x$$So, the term we need to add is $-\frac{1}{3}x$.
### Examples
Imagine you're adjusting a recipe. You have $\frac{5}{6}$ of a cup of flour but the recipe calls for only $\frac{1}{2}$ cup. To find out how much flour to remove, you solve a similar problem. This helps in adjusting quantities to match desired outcomes, whether in cooking, mixing chemicals, or managing resources.
- Isolate $T$: $T = (\frac{1}{2} x - 4) - (\frac{5}{6} x - 4)$.
- Simplify the expression: $T = \frac{1}{2} x - 4 - \frac{5}{6} x + 4$.
- Combine like terms and simplify: $T = -\frac{1}{3} x$.
$\boxed{-\frac{1}{3} x}$
### Explanation
1. Understanding the Problem
We are given the expression $\frac{5}{6} x-4$ and we want to find a term, let's call it $T$, that when added to this expression, results in $\frac{1}{2} x-4$. This can be written as an equation:$$\frac{5}{6} x - 4 + T = \frac{1}{2} x - 4$$
2. Isolating the Unknown Term
To find $T$, we need to isolate it on one side of the equation. We can do this by subtracting $\frac{5}{6} x - 4$ from both sides:$$T = (\frac{1}{2} x - 4) - (\frac{5}{6} x - 4)$$
3. Simplifying the Expression
Now, let's simplify the expression for $T$ by distributing the negative sign and combining like terms:$$T = \frac{1}{2} x - 4 - \frac{5}{6} x + 4$$$$T = (\frac{1}{2} x - \frac{5}{6} x) + (-4 + 4)$$
4. Combining Like Terms
To combine the $x$ terms, we need a common denominator. The least common denominator for 2 and 6 is 6. So, we rewrite $\frac{1}{2} x$ as $\frac{3}{6} x$:$$T = (\frac{3}{6} x - \frac{5}{6} x) + 0$$$$T = -\frac{2}{6} x$$
5. Final Simplification
Finally, we simplify the fraction:$$T = -\frac{1}{3} x$$So, the term we need to add is $-\frac{1}{3}x$.
### Examples
Imagine you're adjusting a recipe. You have $\frac{5}{6}$ of a cup of flour but the recipe calls for only $\frac{1}{2}$ cup. To find out how much flour to remove, you solve a similar problem. This helps in adjusting quantities to match desired outcomes, whether in cooking, mixing chemicals, or managing resources.
