Question

which set of algebra tiles represents the equation $x + 8 = 13$? four sets of algebra tile diagrams are shown, each with a green tile labeled x, several yellow tiles labeled 1, and an equals sign separating left and right sides

Explanation:

Step1: Analyze left side of equation

The left side of \( x + 8 = 13 \) has \( x \) and 8 unit tiles. So we need a set with 1 \( x \)-tile and 8 unit tiles on the left.

Step2: Analyze right side of equation

The right side is 13, so we need 13 unit tiles on the right.

Step3: Check each option

• First option: Left has \( x \) and \( 3 + 3+ 2 = 8 \) unit tiles? Wait, count the first left: \( x \) and \( 3+3 + 2=8 \)? Wait, first left: top row 3, middle 3, bottom 2: \( 3 + 3+ 2 = 8 \). Right: \( 5+5 + 3=15 \)? No, wait first right: 3 rows of 5? Wait no, first right: 3 rows, each 5? Wait no, first right: top 5, middle 5, bottom 5: \( 5\times3 = 15 \). No. Wait wait, let's recount. Wait the equation is \( x + 8 = 13 \), so left: \( x \) + 8 units, right: 13 units.

Wait let's check each:

First set: Left: \( x \) + (3 + 3 + 2) = \( x + 8 \)? Wait top row 3, middle 3, bottom 2: 3+3+2=8. Right: top 5, middle 5, bottom 5: 15. No.

Second set: Left: \( x \) + (3 + 3 + 2)=8? Wait no, left: top 3, middle 3, bottom 2: 8? Wait no, second left: top 3, middle 3, bottom 2: 8? Right: 6 units (2+2+2). No.

Third set: Left: \( x \) + 8? Wait left: top 3, middle 3, bottom 2: 8. Right: 4 units (2+1+1). No.

Fourth set: Left: \( x \) + (3 + 3 + 2)=8? Wait top 3, middle 3, bottom 2: 8. Right: top 5, middle 4, bottom 4? Wait no, fourth right: top 5, middle 4, bottom 4: 5+4+4=13. Yes! Wait left: \( x \) + 8 (3+3+2=8), right: 5+4+4=13? Wait no, let's count the fourth set:

Left: \( x \) tile + (top 3, middle 3, bottom 2) = \( x + 8 \).

Right: top row 5, middle row 4, bottom row 4? Wait no, fourth right: top 5, middle 4, bottom 4? Wait 5 + 4 + 4 = 13. Yes. Wait the fourth set: left is \( x + 8 \), right is 13. So that's the one. Wait but let's check again. Wait the equation is \( x + 8 = 13 \), so left: \( x \) + 8 units, right: 13 units.

Wait the fourth set: left: \( x \) + (3 + 3 + 2) = \( x + 8 \). Right: 5 (top) + 4 (middle) + 4 (bottom) = 13. Yes. So the fourth set (the last one) represents \( x + 8 = 13 \). Wait but in the options, the fourth is the bottom one. Wait the options are:

First: top set.

Second: second from top.

Third: third from top.

Fourth: bottom set.

So the correct one is the bottom set (fourth option). Wait but let's confirm:

Left side: \( x \) + 8 unit tiles (3 + 3 + 2 = 8).

Right side: 13 unit tiles (5 + 4 + 4 = 13). Yes, that matches \( x + 8 = 13 \).

Answer:

The bottom - most set of algebra tiles (the fourth set from the top)