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's define the unknown number as \( x \).

According to the problem, we have the following equation:

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

Now, we will simplify both sides of the equation.

1. Left side:
\[
4(x + 4) = 4x + 16
\]

2. Right side:
\[
2(3x - 2) = 6x - 4
\]

Now we can set the two sides of the equation equal to each other:
\[
4x + 16 = 6x - 4
\]

Next, we will solve for \( x \).

Subtract \( 4x \) from both sides:
\[
16 = 2x - 4
\]

Now add \( 4 \) to both sides:
\[
20 = 2x
\]

Finally, divide both sides by \( 2 \):
\[
x = 10
\]

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