Question

which equation does this set of algebra tiles represent? x + 1 + 1 = 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 (options: x + 1 = 8, x + 1 = 10, x + 2 = 8, x + 2 = 10)

Explanation:

Step1: Count tiles on left

Left side: 1 green tile (\(x\)) + 2 orange tiles (1s) → \(x + 2\).

Step2: Count tiles on right

Right side: Count orange tiles: 4 + 3 + 3? Wait, no—look at the grid. Top row: 4, middle: 3, bottom: 3? Wait, no, the right side has 4 + 3 + 3? Wait, no, let's count again. The right side: first row 4, second 3, third 3? Wait, no, the image shows right side: top row 4, middle 3, bottom 3? Wait, no, actually, let's count the orange tiles. The left side: \(x\) (green) + 2 orange (1s). The right side: let's count the orange tiles. Top row: 4, middle: 3, bottom: 3? Wait, no, 4 + 3 + 3 = 10? Wait, no, maybe I miscounted. Wait, the left side: 1 \(x\) and 2 ones (since two orange 1s). The right side: let's count the orange tiles. Let's see the right side: first row (top) has 4, second row 3, third row 3. 4 + 3 + 3 = 10? Wait, no, 4 + 3 is 7, plus 3 is 10? Wait, but the options are \(x + 2 = 10\)? Wait, no, wait the left side: \(x\) (green) and two 1s (orange), so \(x + 2\). The right side: let's count the orange tiles. Let's look again. The right side: top row: 4, middle row: 3, bottom row: 3. 4 + 3 + 3 = 10? Wait, but maybe I made a mistake. Wait, the left side: \(x\) (1 tile) + 2 (two 1s) → \(x + 2\). The right side: how many 1s? Let's count the orange squares. Top row: 4, middle: 3, bottom: 3. 4 + 3 + 3 = 10? Wait, but the options are \(x + 2 = 10\) (fourth option) or \(x + 2 = 8\)? Wait, maybe I miscounted the right side. Wait, top row: 4, middle: 3, bottom: 3? No, maybe top row 4, middle 3, bottom 3 is 10? Wait, no, 4 + 3 + 3 is 10. But wait, the left side is \(x + 2\), right side is 10? So equation is \(x + 2 = 10\)? Wait, but let's check the options. The options are:

1. \(x + 1 = 8\)

1. \(x + 1 = 10\)

1. \(x + 2 = 8\)

1. \(x + 2 = 10\)

Wait, maybe I miscounted the left side. The left side: \(x\) (green) and two orange 1s? Wait, the left side has a green tile (\(x\)) and two orange 1s (since two small orange squares). So \(x + 2\). The right side: let's count the orange squares. Let's see the right side: top row (first row) 4, middle row 3, bottom row 3. 4 + 3 + 3 = 10. So \(x + 2 = 10\). Wait, but maybe the right side is 8? Wait, 4 + 3 + 1? No, the image shows three rows. Wait, maybe the right side is 4 + 3 + 1? No, the bottom row has three. Wait, maybe I made a mistake. Wait, let's count again. Left side: \(x\) (1) + 2 (two 1s) → \(x + 2\). Right side: 4 (top) + 3 (middle) + 3 (bottom) = 10. So the equation is \(x + 2 = 10\), which is the fourth option.

Step3: Match with options

Left side: \(x + 2\), right side: 10. So the equation is \(x + 2 = 10\).

Answer:

D. \(x + 2 = 10\)