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?
__

Answer 1

Let the unknown number be represented by \( x \).

According to the problem, we can set up the following equation based on the given statement:

1. Four times the sum of a number and four is:
\[
4(x + 4)
\]

2. Two multiplied by two less than three times the number is:
\[
2(3x - 2)
\]

Now, we can set these two expressions equal to each other:
\[
4(x + 4) = 2(3x - 2)
\]

Next, let's simplify both sides of the equation.

Starting with the left side:
\[
4(x + 4) = 4x + 16
\]

Now simplify the right side:
\[
2(3x - 2) = 6x - 4
\]

Now we have the equation:
\[
4x + 16 = 6x - 4
\]

Next, we will isolate \( x \) by first moving all terms involving \( x \) to one side and constant terms to the other side. Subtract \( 4x \) from both sides:
\[
16 = 6x - 4x - 4
\]

This simplifies to:
\[
16 = 2x - 4
\]

Now, add 4 to both sides:
\[
16 + 4 = 2x
\]
\[
20 = 2x
\]

Now, divide both sides by 2:
\[
x = 10
\]

The solution to the problem is:
\[
\boxed{10}
\]