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)
Let's represent the unknown number as "x".
According to the problem, four times the sum of the number and four can be expressed as 4(x + 4).
Similarly, two multiplied by two less than three times the number can be expressed as 2(3x - 2).
Now, we can set up an equation: 4(x + 4) = 2(3x - 2).
Simplifying this equation:
4x + 16 = 6x - 4.
Subtracting 4x from both sides:
16 = 2x - 4.
Adding 4 to both sides:
20 = 2x.
Dividing both sides by 2:
10 = x.
Therefore, the solution to this problem is x = 10.
Let's break down the problem into steps:
Step 1: Assign a variable to the unknown number.
Let's say the unknown number is x.
Step 2: Translate the problem into an equation.
"Four times the sum of a number and four" can be written as 4(x + 4).
"Two multiplied by two less than three times the number" can be written as 2(3x - 2).
Putting it together, we have: 4(x + 4) = 2(3x - 2).
Step 3: Solve the equation.
Distribute on both sides of the equation to simplify it:
4x + 16 = 6x - 4.
Subtract 4x from both sides to move the x terms to one side of the equation:
16 = 2x - 4.
Add 4 to both sides to isolate the x term:
20 = 2x.
Finally, divide both sides by 2 to solve for x:
x = 10.
Step 4: Check the solution.
Plug in the value of x into the original equation to confirm that it works:
4(10 + 4) = 2(3 * 10 - 2).
4(14) = 2(30 - 2).
56 = 2(28).
56 = 56.
The solution to the problem is x = 10.