Certainly! Let's simplify each given pair of expressions step by step.
Pair 1: [tex]\(12x + 8 - 7x - 10\)[/tex]
1. Combine like terms:
- [tex]\(12x - 7x = 5x\)[/tex]
- [tex]\(8 - 10 = -2\)[/tex]
So, the simplified expression is:
[tex]\[ 5x - 2 \][/tex]
Pair 2: [tex]\(\frac{17}{3}x + 17 - \frac{2}{3}x - 15\)[/tex]
1. Combine like terms:
- [tex]\(\frac{17}{3}x - \frac{2}{3}x = \frac{15}{3}x = 5x\)[/tex]
- [tex]\(17 - 15 = 2\)[/tex]
So, the simplified expression is:
[tex]\[ 5x + 2 \][/tex]
Pair 3: [tex]\(8 - 12x - 10 + 7x\)[/tex]
1. Combine like terms:
- [tex]\(-12x + 7x = -5x\)[/tex]
- [tex]\(8 - 10 = -2\)[/tex]
So, the simplified expression is:
[tex]\[ -5x - 2 \][/tex]
Pair 4: [tex]\(9 - \frac{9}{2}x - \frac{1}{2}x - 7\)[/tex]
1. Combine like terms:
- [tex]\(\frac{-9x}{2} + \frac{-1x}{2} = -\frac{10x}{2} = -5x\)[/tex]
- [tex]\(9 - 7 = 2\)[/tex]
So, the simplified expression is:
[tex]\[ 2 - 5x \][/tex]
Now, let’s match these simplified expressions to the given tiles:
Matching:
1. [tex]\( 5x - 2 \)[/tex] matches with [tex]\( 12x + 8 - 7x - 10 \)[/tex]
2. [tex]\( 5x + 2 \)[/tex] matches with [tex]\( \frac{17}{3}x + 17 - \frac{2}{3}x - 15 \)[/tex]
3. [tex]\( -5x - 2 \)[/tex] matches with [tex]\( 8 - 12x - 10 + 7x \)[/tex]
4. [tex]\( 2 - 5x \)[/tex] matches with [tex]\( 9 - \frac{9}{2}x - \frac{1}{2}x - 7 \)[/tex]
So, the correct pairings are:
1. [tex]\( 12x + 8 - 7x - 10 \rightarrow 5x - 2 \)[/tex]
2. [tex]\( \frac{17}{3}x + 17 - \frac{2}{3}x - 15 \rightarrow 5x + 2 \)[/tex]
3. [tex]\( 8 - 12x - 10 + 7x \rightarrow -5x - 2 \)[/tex]
4. [tex]\( 9 - \frac{9}{2}x - \frac{1}{2}x - 7 \rightarrow 2 - 5x \)[/tex]
