Answer :
Let's solve the equation \(4x + 2 = 18\) step-by-step:
1. Identify the equation:
\(4x + 2 = 18\)
2. Isolate the term with the variable:
To do this, use the inverse property of addition to eliminate the constant term on the left side. The inverse property of addition states that we can subtract the same number from both sides of the equation to maintain equality.
Subtract 2 from both sides:
[tex]\[ 4x + 2 - 2 = 18 - 2 \][/tex]
This simplifies to:
[tex]\[ 4x = 16 \][/tex]
3. Solve for the variable:
Now, use the inverse property of multiplication to solve for \(x\). The inverse property of multiplication tells us that we can divide both sides of the equation by the same non-zero number to maintain equality.
Divide both sides by 4:
[tex]\[ \frac{4x}{4} = \frac{16}{4} \][/tex]
This simplifies to:
[tex]\[ x = 4 \][/tex]
Therefore, the properties used to solve the equation \(4x + 2 = 18\) are:
1. The inverse property of addition
2. The inverse property of multiplication
So, the correct answer is the fourth option:
The inverse property of addition and then the inverse property of multiplication
1. Identify the equation:
\(4x + 2 = 18\)
2. Isolate the term with the variable:
To do this, use the inverse property of addition to eliminate the constant term on the left side. The inverse property of addition states that we can subtract the same number from both sides of the equation to maintain equality.
Subtract 2 from both sides:
[tex]\[ 4x + 2 - 2 = 18 - 2 \][/tex]
This simplifies to:
[tex]\[ 4x = 16 \][/tex]
3. Solve for the variable:
Now, use the inverse property of multiplication to solve for \(x\). The inverse property of multiplication tells us that we can divide both sides of the equation by the same non-zero number to maintain equality.
Divide both sides by 4:
[tex]\[ \frac{4x}{4} = \frac{16}{4} \][/tex]
This simplifies to:
[tex]\[ x = 4 \][/tex]
Therefore, the properties used to solve the equation \(4x + 2 = 18\) are:
1. The inverse property of addition
2. The inverse property of multiplication
So, the correct answer is the fourth option:
The inverse property of addition and then the inverse property of multiplication
The answer is D. The inverse property of an addition and inverse property of multiplication. So notice that we have to subtract 2 on both sides. That would be the inverse property of addition. Then we end up with 4x=16 and now we have to divide by 4. Division is the inverse property of multiplication. So the answer is D. Hope this helps!
