Answer :
Certainly! Let's solve each equation step by step and match it to the corresponding solution.
### 1. Solving \(4.5x - 7 = 20\)
1. Add 7 to both sides of the equation to isolate the term with \(x\):
[tex]\[ 4.5x - 7 + 7 = 20 + 7 \][/tex]
Simplifying this, we get:
[tex]\[ 4.5x = 27 \][/tex]
2. Divide both sides by 4.5 to solve for \(x\):
[tex]\[ x = \frac{27}{4.5} \][/tex]
After simplifying, we find:
[tex]\[ x = 6 \][/tex]
So, the solution to the equation \(4.5x - 7 = 20\) is \(x = 6\).
### 2. Solving \(2x + 3 = -7\)
1. Subtract 3 from both sides of the equation to isolate the term with \(x\):
[tex]\[ 2x + 3 - 3 = -7 - 3 \][/tex]
Simplifying this, we get:
[tex]\[ 2x = -10 \][/tex]
2. Divide both sides by 2 to solve for \(x\):
[tex]\[ x = \frac{-10}{2} \][/tex]
After simplifying, we find:
[tex]\[ x = -5 \][/tex]
So, the solution to the equation \(2x + 3 = -7\) is \(x = -5\).
### 3. Solving \(-3x + 7 = 28\)
1. Subtract 7 from both sides of the equation to isolate the term with \(x\):
[tex]\[ -3x + 7 - 7 = 28 - 7 \][/tex]
Simplifying this, we get:
[tex]\[ -3x = 21 \][/tex]
2. Divide both sides by -3 to solve for \(x\):
[tex]\[ x = \frac{21}{-3} \][/tex]
After simplifying, we find:
[tex]\[ x = -7 \][/tex]
So, the solution to the equation \(-3x + 7 = 28\) is \(x = -7\).
### Matching Each Equation to Its Solution
- \(4.5x - 7 = 20\) corresponds to \(x = 6\).
- \(2x + 3 = -7\) corresponds to \(x = -5\).
- \(-3x + 7 = 28\) corresponds to \(x = -7\).
Therefore, the equations matched with their solutions are:
[tex]\[ \begin{array}{ccc} 4.5x - 7 = 20 & \text{corresponds to} & x = 6 \\ 2x + 3 = -7 & \text{corresponds to} & x = -5 \\ -3x + 7 = 28 & \text{corresponds to} & x = -7 \\ \end{array} \][/tex]
### 1. Solving \(4.5x - 7 = 20\)
1. Add 7 to both sides of the equation to isolate the term with \(x\):
[tex]\[ 4.5x - 7 + 7 = 20 + 7 \][/tex]
Simplifying this, we get:
[tex]\[ 4.5x = 27 \][/tex]
2. Divide both sides by 4.5 to solve for \(x\):
[tex]\[ x = \frac{27}{4.5} \][/tex]
After simplifying, we find:
[tex]\[ x = 6 \][/tex]
So, the solution to the equation \(4.5x - 7 = 20\) is \(x = 6\).
### 2. Solving \(2x + 3 = -7\)
1. Subtract 3 from both sides of the equation to isolate the term with \(x\):
[tex]\[ 2x + 3 - 3 = -7 - 3 \][/tex]
Simplifying this, we get:
[tex]\[ 2x = -10 \][/tex]
2. Divide both sides by 2 to solve for \(x\):
[tex]\[ x = \frac{-10}{2} \][/tex]
After simplifying, we find:
[tex]\[ x = -5 \][/tex]
So, the solution to the equation \(2x + 3 = -7\) is \(x = -5\).
### 3. Solving \(-3x + 7 = 28\)
1. Subtract 7 from both sides of the equation to isolate the term with \(x\):
[tex]\[ -3x + 7 - 7 = 28 - 7 \][/tex]
Simplifying this, we get:
[tex]\[ -3x = 21 \][/tex]
2. Divide both sides by -3 to solve for \(x\):
[tex]\[ x = \frac{21}{-3} \][/tex]
After simplifying, we find:
[tex]\[ x = -7 \][/tex]
So, the solution to the equation \(-3x + 7 = 28\) is \(x = -7\).
### Matching Each Equation to Its Solution
- \(4.5x - 7 = 20\) corresponds to \(x = 6\).
- \(2x + 3 = -7\) corresponds to \(x = -5\).
- \(-3x + 7 = 28\) corresponds to \(x = -7\).
Therefore, the equations matched with their solutions are:
[tex]\[ \begin{array}{ccc} 4.5x - 7 = 20 & \text{corresponds to} & x = 6 \\ 2x + 3 = -7 & \text{corresponds to} & x = -5 \\ -3x + 7 = 28 & \text{corresponds to} & x = -7 \\ \end{array} \][/tex]
