Question

simplify each algebraic expression. drag the tiles to the correct boxes to complete the pai
tiles
-5x - 2 5x + 2 5x - 2 -5x + 2
pairs
12x + 8 - 7x - 10
\frac{17}{2}x + 17 - \frac{7}{2}x - 15
8 - 12x - 10 + 7x
9 - \frac{17}{2}x - \frac{7}{2}x - 7
submit

Explanation:

Step1: Simplify \(12x + 8 - 7x - 10\)

Combine like terms: \((12x - 7x)+(8 - 10)=5x - 2\)

Step2: Simplify \(\frac{17}{2}x + 17 - \frac{3}{2}x - 15\)

Combine like terms: \((\frac{17}{2}x-\frac{3}{2}x)+(17 - 15)=7x + 2\)? Wait, no, \(\frac{17}{2}x-\frac{3}{2}x=\frac{14}{2}x = 7x\)? Wait, no, the tiles have \(5x\) terms. Wait, maybe I miscalculated. Wait, \(\frac{17}{2}x-\frac{3}{2}x=\frac{14}{2}x = 7x\)? But the tiles are \(5x\) or \(-5x\). Wait, maybe the second expression is \(\frac{17}{2}x+17-\frac{3}{2}x - 15\). Let's recalculate: \(\frac{17}{2}x-\frac{3}{2}x=\frac{14}{2}x = 7x\)? No, that can't be. Wait, maybe it's a typo, and it's \(\frac{17}{2}x+17-\frac{13}{2}x - 15\). Then \(\frac{17}{2}x-\frac{13}{2}x=\frac{4}{2}x = 2x\)? No, the tiles are \(5x + 2\), \(5x - 2\), \(-5x + 2\), \(-5x - 2\). Let's do the first expression: \(12x + 8 - 7x - 10\). Combine like terms: \(12x - 7x = 5x\), \(8 - 10=-2\). So \(5x - 2\).

Step3: Simplify \(\frac{17}{2}x + 17 - \frac{3}{2}x - 15\). Wait, maybe it's \(\frac{17}{2}x+17-\frac{7}{2}x - 15\)? Then \(\frac{17}{2}x-\frac{7}{2}x=\frac{10}{2}x = 5x\), \(17 - 15 = 2\). So \(5x + 2\).

Step4: Simplify \(8 - 12x - 10 + 7x\). Combine like terms: \(-12x + 7x=-5x\), \(8 - 10=-2\). So \(-5x - 2\).

Step5: Simplify \(9-\frac{1}{2}x-\frac{1}{2}x - 7\). Combine like terms: \(-\frac{1}{2}x-\frac{1}{2}x=-x\)? No, wait, maybe it's \(9-\frac{1}{2}x-\frac{9}{2}x - 7\). Then \(-\frac{1}{2}x-\frac{9}{2}x=-5x\), \(9 - 7 = 2\). So \(-5x + 2\).

So:

1. \(12x + 8 - 7x - 10\) simplifies to \(5x - 2\)
2. \(\frac{17}{2}x + 17 - \frac{3}{2}x - 15\) (assuming it's \(\frac{17}{2}x-\frac{13}{2}x\) was a mistake, and it's \(\frac{17}{2}x-\frac{7}{2}x\)) simplifies to \(5x + 2\)
3. \(8 - 12x - 10 + 7x\) simplifies to \(-5x - 2\)
4. \(9 - \frac{1}{2}x - \frac{9}{2}x - 7\) simplifies to \(-5x + 2\)

So the pairs are:

• \(12x + 8 - 7x - 10\) → \(5x - 2\)
• \(\frac{17}{2}x + 17 - \frac{3}{2}x - 15\) (corrected) → \(5x + 2\)
• \(8 - 12x - 10 + 7x\) → \(-5x - 2\)
• \(9 - \frac{1}{2}x - \frac{9}{2}x - 7\) → \(-5x + 2\)

Answer:

• \(12x + 8 - 7x - 10\) → \(5x - 2\)
• \(\frac{17}{2}x + 17 - \frac{3}{2}x - 15\) → \(5x + 2\) (assuming the x terms combine to 5x)
• \(8 - 12x - 10 + 7x\) → \(-5x - 2\)
• \(9 - \frac{1}{2}x - \frac{9}{2}x - 7\) → \(-5x + 2\)

(Note: The second expression's x - coefficient subtraction should result in 5x, so likely a typo in the original problem's fraction, but based on the tiles, we adjust to get 5x + 2. Similarly, the fourth expression's x - coefficients should add to -5x.)