Let's solve each equation step-by-step and match them to their solutions.
### Equation 1: [tex]\( 4.5x - 7 = 20 \)[/tex]
Step 1: Add 7 to both sides of the equation to isolate the term with [tex]\( x \)[/tex].
[tex]\[ 4.5x - 7 + 7 = 20 + 7 \][/tex]
[tex]\[ 4.5x = 27 \][/tex]
Step 2: Divide both sides by 4.5 to solve for [tex]\( x \)[/tex].
[tex]\[ x = \frac{27}{4.5} \][/tex]
[tex]\[ x = 6 \][/tex]
So, for the equation [tex]\( 4.5x - 7 = 20 \)[/tex], the solution is:
[tex]\[ x = 6 \][/tex]
### Equation 2: [tex]\( -3x + 7 = 28 \)[/tex]
Step 1: Subtract 7 from both sides of the equation to isolate the term with [tex]\( x \)[/tex].
[tex]\[ -3x + 7 - 7 = 28 - 7 \][/tex]
[tex]\[ -3x = 21 \][/tex]
Step 2: Divide both sides by -3 to solve for [tex]\( x \)[/tex].
[tex]\[ x = \frac{21}{-3} \][/tex]
[tex]\[ x = -7 \][/tex]
So, for the equation [tex]\( -3x + 7 = 28 \)[/tex], the solution is:
[tex]\[ x = -7 \][/tex]
### Equation 3: [tex]\( 2x + 3 = -7 \)[/tex]
Step 1: Subtract 3 from both sides of the equation to isolate the term with [tex]\( x \)[/tex].
[tex]\[ 2x + 3 - 3 = -7 - 3 \][/tex]
[tex]\[ 2x = -10 \][/tex]
Step 2: Divide both sides by 2 to solve for [tex]\( x \)[/tex].
[tex]\[ x = \frac{-10}{2} \][/tex]
[tex]\[ x = -5 \][/tex]
So, for the equation [tex]\( 2x + 3 = -7 \)[/tex], the solution is:
[tex]\[ x = -5 \][/tex]
### Matching the Solutions
Now, we match each solution to its corresponding equation:
- [tex]\( (4.5x - 7 = 20) \rightarrow x = 6 \)[/tex]
- [tex]\( (-3x + 7 = 28) \rightarrow x = -7 \)[/tex]
- [tex]\( (2x + 3 = -7) \rightarrow x = -5 \)[/tex]
Thus, the solutions matched to the equations are as follows:
- [tex]\( 4.5x - 7 = 20: \quad x = 6 \)[/tex]
- [tex]\( -3x + 7 = 28: \quad x = -7 \)[/tex]
- [tex]\( 2x + 3 = -7: \quad x = -5 \)[/tex]
