Let's solve each equation one by one to find the value of [tex]\(a\)[/tex].
### Equation 1:
[tex]\[ 6(2a - a + 1) = 24 \][/tex]
Simplify inside the parentheses:
[tex]\[ 6(a + 1) = 24 \][/tex]
Divide both sides by 6:
[tex]\[ a + 1 = 4 \][/tex]
Subtract 1 from both sides:
[tex]\[ a = 3 \][/tex]
### Equation 2:
[tex]\[ 2a + 3(a + 1) = 8 \][/tex]
Distribute 3:
[tex]\[ 2a + 3a + 3 = 8 \][/tex]
Combine like terms:
[tex]\[ 5a + 3 = 8 \][/tex]
Subtract 3 from both sides:
[tex]\[ 5a = 5 \][/tex]
Divide by 5:
[tex]\[ a = 1 \][/tex]
### Equation 3:
[tex]\[ 3a - 2a - 4 = 0 \][/tex]
Combine like terms:
[tex]\[ a - 4 = 0 \][/tex]
Add 4 to both sides:
[tex]\[ a = 4 \][/tex]
### Equation 4:
[tex]\[ 4 + 3(a + 2) = 16 \][/tex]
Distribute 3:
[tex]\[ 4 + 3a + 6 = 16 \][/tex]
Combine constants:
[tex]\[ 3a + 10 = 16 \][/tex]
Subtract 10 from both sides:
[tex]\[ 3a = 6 \][/tex]
Divide by 3:
[tex]\[ a = 2 \][/tex]
### Summary:
So, matching each equation to the value of [tex]\(a\)[/tex] that makes it true:
1. [tex]\( 6(2a - a + 1) = 24 \)[/tex] → [tex]\( a = 3 \)[/tex]
2. [tex]\( 2a + 3(a + 1) = 8 \)[/tex] → [tex]\( a = 1 \)[/tex]
3. [tex]\( 3a - 2a - 4 = 0 \)[/tex] → [tex]\( a = 4 \)[/tex]
4. [tex]\( 4 + 3(a + 2) = 16 \)[/tex] → [tex]\( a = 2 \)[/tex]
So, the matches are:
- [tex]\( 3a - 2a - 4 = 0 \)[/tex] → 4
- [tex]\( 6(2a - a + 1) = 24 \)[/tex] → 3
- [tex]\( 4 + 3(a + 2) = 16 \)[/tex] → 2
- [tex]\( 2a + 3(a + 1) = 8 \)[/tex] → 1
