Question

what is the value of x in the equation represented by the tiles? left: three rectangles labeled (-x), four squares labeled (1); right: two rectangles labeled (-x), one square labeled (1)
options: (3), (5), (-3), (-1)

Explanation:

Step1: Translate tiles to equation

Left side: \( 3(-x) + 4(1) \), Right side: \( 2(-x) + 1(1) \). So equation: \( -3x + 4 = -2x + 1 \)

Step2: Add \( 3x \) to both sides

\( -3x + 4 + 3x = -2x + 1 + 3x \) → \( 4 = x + 1 \)

Step3: Subtract 1 from both sides

\( 4 - 1 = x + 1 - 1 \) → \( 3 = x \) → \( x = 3 \) (Wait, no, wait. Wait, let's recheck. Wait, left side: three -x tiles and four 1 tiles. So \( -3x + 4 \). Right side: two -x tiles and one 1 tile. So \( -2x + 1 \). Then, \( -3x + 4 = -2x + 1 \). Let's solve: add \( 3x \) to both sides: \( 4 = x + 1 \). Subtract 1: \( x = 3 \)? But wait, maybe I messed up signs. Wait, no, the tiles: -x is negative x. Wait, let's do again. Equation: \( -3x + 4 = -2x + 1 \). Subtract \( -2x \) (or add 2x) to both sides: \( -3x + 2x + 4 = 1 \) → \( -x + 4 = 1 \). Subtract 4: \( -x = -3 \). Multiply by -1: \( x = 3 \)? Wait, but the options have 3. Wait, but let's check again. Wait, left: 3(-x) + 41 = -3x +4. Right: 2(-x) +11 = -2x +1. So equation: -3x +4 = -2x +1. Let's move variables to left and constants to right: -3x +2x = 1 -4 → -x = -3 → x = 3. Yes. Wait, but the options have 3 as first option. Wait, but maybe I made a mistake. Wait, no, let's check the tiles again. Left: three -x (so -3x) and four 1s (so +4). Right: two -x (so -2x) and one 1 (so +1). So equation is -3x +4 = -2x +1. Solving: add 3x to both sides: 4 = x +1. Subtract 1: x=3. So answer is 3. Wait, but let me check again. Wait, maybe the tiles are positive x? No, the tiles are labeled -x. So -x is negative x. So the equation is correct. So x=3.

Answer:

3 (corresponding to the first option: 3)