Question

solve the equation for \\(x\\) from todays warm up, \\(3x + 2 = x + 5\\), and find the weight of the square.

a the square weighs \\(\frac{3}{2}\\).
b the square weighs \\(\frac{7}{2}\\).
c the square weighs \\(\frac{2}{3}\\).
d the square weighs 2.

Explanation:

Identify the given equation

The problem asks us to solve the equation \(3x + 2 = x + 5\), which represents the balanced scale shown in the image.

Subtract x from both sides

To group the variable terms, we subtract \(x\) from both sides of the equation:

$$ (3x - x) + 2 = 5 $$

$$ 2x + 2 = 5 $$

Subtract 2 from both sides

To isolate the variable term, we subtract \(2\) from both sides:

$$ 2x = 5 - 2 $$

$$ 2x = 3 $$

Solve for x

To find the value of \(x\), which represents the weight of the square, we divide both sides by \(2\):

$$ x = \frac{3}{2} $$

Match with the options

The weight of the square is \(x = \frac{3}{2}\). This matches option B: "The square weighs \(\frac{3}{2}\)."

Answer:

• (A) The square weighs \(\frac{2}{3}\).
• (B) The square weighs \(\frac{3}{2}\). (Correct answer)
• (C) The square weighs \(\frac{7}{2}\).
• (D) The square weighs 2.