Linear Equations in Real-World Scenarios Practice

Question

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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)

Answer 1

Let's translate the problem into a mathematical equation.

1. Let the unknown number be represented by \( x \).
2. The sum of the number and four can be expressed as \( x + 4 \).
3. Four times this sum would be \( 4(x + 4) \).

On the other side:

1. Three times the number is \( 3x \).
2. Two less than this quantity is \( 3x - 2 \).
3. Two multiplied by this result gives \( 2(3x - 2) \).

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

Now, let's solve the equation step by step.

1. Distribute on both sides: \[ 4x + 16 = 6x - 4 \]

2. Get all terms involving \( x \) on one side and constant terms on the other: \[ 4x - 6x = -4 - 16 \] \[ -2x = -20 \]

3. Divide by -2: \[ x = 10 \]

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