Answer :
Let's solve the equation step by step, matching each step to its justification.
### Given:
[tex]\[2x + 5 = 19 \][/tex]
### Step 1: Apply the given information
[tex]\[ 2x + 5 = 19 \][/tex]
_Justification:_ This is the given equation.
### Step 2: Subtract 5 from both sides of the equation to isolate the term with [tex]\( x \)[/tex].
[tex]\[ 2x + 5 - 5 = 19 - 5 \][/tex]
_Justification:_ Subtraction property of equality. We subtract the same number (5) from both sides to maintain the equality.
### Step 3: Simplify the equation
[tex]\[ 2x = 14 \][/tex]
_Justification:_ After subtracting 5 from both sides, we are left with [tex]\( 2x = 14 \)[/tex].
### Step 4: Divide both sides by 2 to solve for [tex]\( x \)[/tex]
[tex]\[ \frac{2x}{2} = \frac{14}{2} \][/tex]
_Justification:_ Division property of equality. We divide both sides by 2 to isolate [tex]\( x \)[/tex].
### Step 5: Simplify the division
[tex]\[ x = 7 \][/tex]
_Justification:_ After dividing both sides by 2, we are left with [tex]\( x = 7 \)[/tex].
Now, let’s match each step with the provided justifications:
1. [tex]$2 x+5=19 \rightarrow$[/tex] given
2. [tex]$2 x+5-5=19-5 \rightarrow$[/tex] subtraction property of equality
3. [tex]$2 x=14 \rightarrow$[/tex] subtract
4. [tex]$2 x / 2=14 / 2 \rightarrow$[/tex] divide
5. [tex]$x=7 \rightarrow$[/tex] division property of equality
Each step corresponds correctly to the given justification.
### Given:
[tex]\[2x + 5 = 19 \][/tex]
### Step 1: Apply the given information
[tex]\[ 2x + 5 = 19 \][/tex]
_Justification:_ This is the given equation.
### Step 2: Subtract 5 from both sides of the equation to isolate the term with [tex]\( x \)[/tex].
[tex]\[ 2x + 5 - 5 = 19 - 5 \][/tex]
_Justification:_ Subtraction property of equality. We subtract the same number (5) from both sides to maintain the equality.
### Step 3: Simplify the equation
[tex]\[ 2x = 14 \][/tex]
_Justification:_ After subtracting 5 from both sides, we are left with [tex]\( 2x = 14 \)[/tex].
### Step 4: Divide both sides by 2 to solve for [tex]\( x \)[/tex]
[tex]\[ \frac{2x}{2} = \frac{14}{2} \][/tex]
_Justification:_ Division property of equality. We divide both sides by 2 to isolate [tex]\( x \)[/tex].
### Step 5: Simplify the division
[tex]\[ x = 7 \][/tex]
_Justification:_ After dividing both sides by 2, we are left with [tex]\( x = 7 \)[/tex].
Now, let’s match each step with the provided justifications:
1. [tex]$2 x+5=19 \rightarrow$[/tex] given
2. [tex]$2 x+5-5=19-5 \rightarrow$[/tex] subtraction property of equality
3. [tex]$2 x=14 \rightarrow$[/tex] subtract
4. [tex]$2 x / 2=14 / 2 \rightarrow$[/tex] divide
5. [tex]$x=7 \rightarrow$[/tex] division property of equality
Each step corresponds correctly to the given justification.
