Question

which sum or difference is modeled by the algebra tiles? image of algebra tiles: 5 blue x tiles, 7 red -1 tiles select the correct answer. option 1: (-2x + 3) + (3x - 4) option 2: (-2x + 3) - (3x - 4) option 3: (2x - 3) + (-3x + 4) option 4: (2x - 3) - (-3x + 4)

Explanation:

Step1: Analyze the algebra tiles

The blue tiles represent positive \(x\) terms. There are 5 blue \(x\) tiles? Wait, no, wait. Wait, looking at the options, let's re - evaluate. Wait, the first part: let's count the \(x\) terms and the constant terms. Wait, the blue tiles: wait, maybe I misread. Wait, the first option: \((-2x + 3)+(3x - 4)\). Let's simplify each option.

Step2: Simplify Option 1: \((-2x + 3)+(3x - 4)\)

Combine like terms: \(-2x+3x+3 - 4=x - 1\). No, that's not matching the tiles. Wait, maybe I made a mistake in counting the tiles. Wait, the algebra tiles: blue tiles (positive \(x\)): let's see the options. Wait, the first option: \((-2x + 3)+(3x - 4)\). Let's expand it: \(-2x+3 + 3x-4=x - 1\).

Wait, maybe I should count the tiles again. The blue tiles: wait, the first part of the tiles: 5 blue \(x\)? No, wait the options have coefficients like - 2x, 3x, etc. Wait, maybe the blue tiles are positive \(x\) and the red are negative 1s. Wait, the number of \(x\) terms: let's look at the options.

Wait, let's simplify each option:

Option 1: \((-2x + 3)+(3x - 4)=(-2x+3x)+(3 - 4)=x - 1\)

Option 2: \((-2x + 3)-(3x - 4)=-2x + 3-3x + 4=-5x+7\)

Option 3: \((2x - 3)+(-3x + 4)=2x-3-3x + 4=-x + 1\)

Option 4: \((2x - 3)-(-3x + 4)=2x-3 + 3x-4=5x-7\)

Wait, now looking at the algebra tiles: there are 5 positive \(x\) tiles (blue) and 7 negative 1 tiles (red)? Wait, no, the red tiles: first row 3, second row 4, total 7 negative 1s. And the \(x\) tiles: 5 positive \(x\)s? Wait, no, the first option: \((-2x + 3)+(3x - 4)\): - 2x+3x = x, 3 - 4=-1. No. Wait, the fourth option: \((2x - 3)-(-3x + 4)=2x-3 + 3x-4=5x-7\). Which matches the tiles: 5 positive \(x\)s and 7 negative 1s. Wait, no, the red tiles are 7 negative 1s (since 3 + 4 = 7) and the blue tiles are 5 positive \(x\)s. Wait, the fourth option simplifies to \(5x-7\), which is 5 positive \(x\) terms and 7 negative 1 terms. Let's check the other options:

Option 1: \((-2x + 3)+(3x - 4)=x - 1\) (1x and - 1)

Option 2: \((-2x + 3)-(3x - 4)=-5x + 7\) ( - 5x and +7)

Option 3: \((2x - 3)+(-3x + 4)=-x + 1\) ( - x and +1)

Option 4: \((2x - 3)-(-3x + 4)=2x-3 + 3x-4=5x-7\) (5x and - 7)

Which matches the tiles: 5 positive \(x\) tiles and 7 negative 1 tiles. So the correct option is the fourth one? Wait, no, wait the first option: \((-2x + 3)+(3x - 4)\). Wait, maybe I messed up the sign of the tiles. Wait, the blue tiles are positive \(x\), red are negative 1. So the expression should be a combination that gives 5x - 7. Let's re - check the fourth option: \((2x - 3)-(-3x + 4)=2x-3 + 3x-4=5x-7\). Yes, that's 5x (positive) and - 7 (negative 1s, 7 of them). So the correct answer is the fourth option. Wait, but let's check the first option again. Wait, maybe I made a mistake in the tile count. Wait, the first option: \((-2x + 3)+(3x - 4)=x - 1\). No. The fourth option: \((2x - 3)-(-3x + 4)=5x-7\), which has 5x and - 7, matching the 5 blue \(x\) tiles and 7 red (-1) tiles.

Answer:

\((2x - 3)-(-3x + 4)\) (the fourth option)