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Answer :
Sure! Let's go through the steps to solve the equation [tex]\(7(x-2) = x + 16\)[/tex] and prove that [tex]\(x = 5\)[/tex].
### Step-by-Step Solution
Statement 1: [tex]\( 7(x - 2) = x + 16 \)[/tex]
This is the given equation we want to solve.
Statement 2: [tex]\( 7x - 14 = x + 16 \)[/tex]
Reason: Distribute the 7 to both terms inside the parenthesis.
When distributing, we get:
[tex]\[ 7(x - 2) = 7x - 14 \][/tex]
Statement 3: [tex]\( 7x - 14 + 14 = x + 16 + 14 \)[/tex]
Reason: Add 14 to both sides to simplify.
To isolate the term with [tex]\(x\)[/tex], we add 14 to both sides:
[tex]\[ 7x - 14 + 14 = x + 16 + 14 \][/tex]
[tex]\[ 7x = x + 30 \][/tex]
Statement 4: [tex]\( 7x - x = x + 30 - x \)[/tex]
Reason: Subtract [tex]\(x\)[/tex] from both sides to consolidate the [tex]\(x\)[/tex] terms on one side.
Subtract [tex]\(x\)[/tex] from both sides to get:
[tex]\[ 7x - x = x + 30 - x \][/tex]
[tex]\[ 6x = 30 \][/tex]
Statement 5: [tex]\( 6x = 30 \)[/tex]
Reason: Simplify the expression after subtraction.
Now we have:
[tex]\[ 6x = 30 \][/tex]
Final Step: Solve for [tex]\(x\)[/tex]
To find [tex]\(x\)[/tex], divide both sides by 6:
[tex]\[ x = \frac{30}{6} \][/tex]
[tex]\[ x = 5 \][/tex]
So, the solution to the equation [tex]\(7(x-2) = x + 16\)[/tex] is [tex]\(x = 5\)[/tex].
### Step-by-Step Solution
Statement 1: [tex]\( 7(x - 2) = x + 16 \)[/tex]
This is the given equation we want to solve.
Statement 2: [tex]\( 7x - 14 = x + 16 \)[/tex]
Reason: Distribute the 7 to both terms inside the parenthesis.
When distributing, we get:
[tex]\[ 7(x - 2) = 7x - 14 \][/tex]
Statement 3: [tex]\( 7x - 14 + 14 = x + 16 + 14 \)[/tex]
Reason: Add 14 to both sides to simplify.
To isolate the term with [tex]\(x\)[/tex], we add 14 to both sides:
[tex]\[ 7x - 14 + 14 = x + 16 + 14 \][/tex]
[tex]\[ 7x = x + 30 \][/tex]
Statement 4: [tex]\( 7x - x = x + 30 - x \)[/tex]
Reason: Subtract [tex]\(x\)[/tex] from both sides to consolidate the [tex]\(x\)[/tex] terms on one side.
Subtract [tex]\(x\)[/tex] from both sides to get:
[tex]\[ 7x - x = x + 30 - x \][/tex]
[tex]\[ 6x = 30 \][/tex]
Statement 5: [tex]\( 6x = 30 \)[/tex]
Reason: Simplify the expression after subtraction.
Now we have:
[tex]\[ 6x = 30 \][/tex]
Final Step: Solve for [tex]\(x\)[/tex]
To find [tex]\(x\)[/tex], divide both sides by 6:
[tex]\[ x = \frac{30}{6} \][/tex]
[tex]\[ x = 5 \][/tex]
So, the solution to the equation [tex]\(7(x-2) = x + 16\)[/tex] is [tex]\(x = 5\)[/tex].
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