Answer :
Let's solve the given equations one by one and match them to the correct solutions.
1. Equation: 4(3x + 5) - 3 = 9z - 7
- Solution: The x-value that satisfies this equation when expressed in terms of z is [tex]\([\frac{9z}{16} - \frac{7}{2}]\)[/tex]. Notice that this means x is expressed in terms of z. So, there isn't a single numerical value for x, but rather a relationship between x and z.
2. Equation: 5(x + 7) - 3(x - 4) = 7x + 2
- By solving this equation, we find [tex]\( x = 9 \)[/tex].
3. Equation: \frac{1}{3}(5z - 9) = 2\left(\frac{1}{3}z + 6\right)
- Solving for z, we get [tex]\( z = 15 \)[/tex].
Given the results we obtained:
- The equation [tex]\( 4(3x + 5) - 3 = 9z - 7 \)[/tex] pairs with [tex]\( \frac{9z}{16} - \frac{7}{2} \)[/tex].
- The equation [tex]\( 5(x + 7) - 3(x - 4) = 7x + 2 \)[/tex] pairs with [tex]\( x = 9 \)[/tex].
- The equation [tex]\( \frac{1}{3}(5z - 9) = 2\left(\frac{1}{3}z + 6\right) \)[/tex] pairs with [tex]\( z = 15 \)[/tex].
Now, let's match this with the given tiles:
- For the equation [tex]\( 4(3x + 5) - 3 = 9z - 7 \)[/tex]:
- This equation does not have a single numerical x-value in the given options since x depends on z. The solution is [tex]\( \frac{9z}{16} - \frac{7}{2} \)[/tex], but this form matches none of the provided x-values exactly.
- For the equation [tex]\( 5(x + 7) - 3(x - 4) = 7x + 2 \)[/tex]:
- We have [tex]\( x = 9 \)[/tex]. So, match this to [tex]\( x = 9 \)[/tex].
- For the equation [tex]\( \frac{1}{3}(5z - 9) = 2\left(\frac{1}{3}z + 6\right) \)[/tex]:
- We have [tex]\( z = 15 \)[/tex]. So, match this to [tex]\( z = 15 \)[/tex].
Valid matches:
- [tex]\( 4(3x + 5) - 3 = 9z - 7 \)[/tex]: [No direct numerical match]
- [tex]\( 5(x + 7) - 3(x - 4) = 7x + 2 \)[/tex]: [tex]\( x = 9 \)[/tex]
- [tex]\( \frac{1}{3}(5z - 9) = 2\left(\frac{1}{3}z + 6\right) \)[/tex]: [tex]\( z = 15 \)[/tex]
Thus:
- [tex]\( \underline{4(3x + 5) - 3 = 9z - 7 \)[/tex] belongs here}
- [tex]\(5(x + 7) - 3(x - 4) = 7x + 2 \longrightarrow x=9\)[/tex]
- [tex]\( \frac{1}{3}(5z - 9) = 2\left(\frac{1}{3}z + 6\right) \longrightarrow z=15\)[/tex]
1. Equation: 4(3x + 5) - 3 = 9z - 7
- Solution: The x-value that satisfies this equation when expressed in terms of z is [tex]\([\frac{9z}{16} - \frac{7}{2}]\)[/tex]. Notice that this means x is expressed in terms of z. So, there isn't a single numerical value for x, but rather a relationship between x and z.
2. Equation: 5(x + 7) - 3(x - 4) = 7x + 2
- By solving this equation, we find [tex]\( x = 9 \)[/tex].
3. Equation: \frac{1}{3}(5z - 9) = 2\left(\frac{1}{3}z + 6\right)
- Solving for z, we get [tex]\( z = 15 \)[/tex].
Given the results we obtained:
- The equation [tex]\( 4(3x + 5) - 3 = 9z - 7 \)[/tex] pairs with [tex]\( \frac{9z}{16} - \frac{7}{2} \)[/tex].
- The equation [tex]\( 5(x + 7) - 3(x - 4) = 7x + 2 \)[/tex] pairs with [tex]\( x = 9 \)[/tex].
- The equation [tex]\( \frac{1}{3}(5z - 9) = 2\left(\frac{1}{3}z + 6\right) \)[/tex] pairs with [tex]\( z = 15 \)[/tex].
Now, let's match this with the given tiles:
- For the equation [tex]\( 4(3x + 5) - 3 = 9z - 7 \)[/tex]:
- This equation does not have a single numerical x-value in the given options since x depends on z. The solution is [tex]\( \frac{9z}{16} - \frac{7}{2} \)[/tex], but this form matches none of the provided x-values exactly.
- For the equation [tex]\( 5(x + 7) - 3(x - 4) = 7x + 2 \)[/tex]:
- We have [tex]\( x = 9 \)[/tex]. So, match this to [tex]\( x = 9 \)[/tex].
- For the equation [tex]\( \frac{1}{3}(5z - 9) = 2\left(\frac{1}{3}z + 6\right) \)[/tex]:
- We have [tex]\( z = 15 \)[/tex]. So, match this to [tex]\( z = 15 \)[/tex].
Valid matches:
- [tex]\( 4(3x + 5) - 3 = 9z - 7 \)[/tex]: [No direct numerical match]
- [tex]\( 5(x + 7) - 3(x - 4) = 7x + 2 \)[/tex]: [tex]\( x = 9 \)[/tex]
- [tex]\( \frac{1}{3}(5z - 9) = 2\left(\frac{1}{3}z + 6\right) \)[/tex]: [tex]\( z = 15 \)[/tex]
Thus:
- [tex]\( \underline{4(3x + 5) - 3 = 9z - 7 \)[/tex] belongs here}
- [tex]\(5(x + 7) - 3(x - 4) = 7x + 2 \longrightarrow x=9\)[/tex]
- [tex]\( \frac{1}{3}(5z - 9) = 2\left(\frac{1}{3}z + 6\right) \longrightarrow z=15\)[/tex]
