Question

Four times the sum of a number and four is the same as two multiplied by two less than three times the number. What is the solution to this problem?(1 point) __

Answer 1

Let the unknown number be represented by \( x \). We can translate the problem statement into an equation.

The first part of the statement is "four times the sum of a number and four", which can be expressed as:

\[
4(x + 4)
\]

The second part is "two multiplied by two less than three times the number", which can be expressed as:

\[
2(3x - 2)
\]

Now we can set the two expressions equal to each other, creating the equation:

\[
4(x + 4) = 2(3x - 2)
\]

Next, we will simplify both sides of the equation.

Starting with the left-hand side:

\[
4(x + 4) = 4x + 16
\]

Now simplifying the right-hand side:

\[
2(3x - 2) = 6x - 4
\]

Now we have the equation:

\[
4x + 16 = 6x - 4
\]

To solve for \( x \), we will first move the \( 6x \) term to the left side by subtracting \( 6x \) from both sides:

\[
4x - 6x + 16 = -4
\]
\[
-2x + 16 = -4
\]

Next, we will isolate the \( -2x \) term by subtracting 16 from both sides:

\[
-2x = -4 - 16
\]
\[
-2x = -20
\]

Now, divide both sides by -2:

\[
x = \frac{-20}{-2}
\]
\[
x = 10
\]

Thus, the solution to the problem is:

\[
\boxed{10}
\]