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)
Remaining Attempts : 3

Answer 1

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

According to the problem, we can set up the equation based on the description provided:

1. "Four times the sum of a number and four" can be expressed as:
\[
4(x + 4)
\]

2. "Two multiplied by two less than three times the number" can be expressed as:
\[
2(3x - 2)
\]

Now we can set up the equation based on these two expressions:
\[
4(x + 4) = 2(3x - 2)
\]

Now, let's simplify both sides of the equation:

1. Expanding the left side:
\[
4x + 16
\]

2. Expanding the right side:
\[
6x - 4
\]

Putting it all together, we have:
\[
4x + 16 = 6x - 4
\]

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

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

2. Add \( 4 \) to both sides:
\[
20 = 2x
\]

3. Divide both sides by \( 2 \):
\[
x = 10
\]

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