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 call the number "x". The given equation can be written as follows:
4(x + 4) = 2(3x - 2)
Now, let's simplify and solve for x:
4x + 16 = 6x - 4
Subtract 4x from both sides:
16 = 2x - 4
Add 4 to both sides:
20 = 2x
Divide both sides by 2:
x = 10
Therefore, the solution to this problem is x = 10.
A string is cut in two so that one section is 5 inches longer than the other. Twice the length of the longer section is three times the length of the shorter section. Write an equation that allows you to solve for the length of the shorter section. How long is the shorter section?(1 point)
Responses
To solve this problem, let's first translate the given problem into an equation.
Let's assume the number is represented by x.
According to the problem, "Four times the sum of a number and four is the same as two multiplied by two less than three times the number."
This can be written as:
4(x + 4) = 2(3x - 2)
Now we can solve the equation step by step:
First, distribute:
4x + 16 = 6x - 4
Next, subtract 4x from both sides to isolate the variable on one side:
16 = 2x - 4
Adding 4 to both sides:
20 = 2x
Finally, divide both sides by 2 to solve for x:
x = 10
Therefore, the solution to the problem is x = 10.
To solve this problem, let's first translate the given information into an equation.
Let's assume the number is represented by "x".
According to the problem, "Four times the sum of a number and four" can be represented as "4(x + 4)".
And "two multiplied by two less than three times the number" can be represented as "2(3x - 2)".
Now we can set up the equation:
4(x + 4) = 2(3x - 2)
Next, we can simplify the equation:
4x + 16 = 6x - 4
Let's isolate the variable by subtracting 4x from both sides:
4x - 4x + 16 = 6x - 4x - 4
16 = 2x - 4
Now, let's further isolate the variable by adding 4 to both sides:
16 + 4 = 2x - 4 + 4
20 = 2x
Finally, divide both sides of the equation by 2 to solve for x:
20/2 = 2x/2
10 = x
Therefore, the solution to the problem is x = 10.