This question tests understanding that subtraction p-q equals adding the additive inverse p+(-q), and the distance between numbers as |p-q| (absolute value of the difference). Subtraction as addition: p-q = p+(-q) by definition (subtracting q means adding the opposite -q: 5-8=5+(-8)=-3, or 7-(-3)=7+3=10 since subtracting a negative adds the positive). On the number line, p-q starts at p and moves distance |q| left if q>0 (subtracting positive), or right if q<0 (subtracting negative = adding positive); distance between p and q is |p-q|=|q-p| (absolute value of the difference, always positive: |3-10|=|-7|=7 units apart, or |10-3|=7). For example, 15-20 can be rewritten as 15+(-20)=-5 (temperature drops from 15°C to -5°C), or distance from -4 to 3: |3-(-4)|=|3+4|=7 units (or |-4-3|=|-7|=7), or 10-25 for money: 10+(-25)=-15 (debt of $15). The correct rewriting for 10-25 is 10+(-25)=-15, interpreting as short $15 coins (negative balance), as in choice A. A common error is misapplying signs in context, like choice B adding positive 25 to get 35 (positive balance instead of debt), or choice C with incorrect sum of -15 as 15, or choice D subtracting -25 which adds 25 incorrectly. Using the additive inverse, rewrite every subtraction as addition (p-q→p+(-q), making all operations additions), and apply addition rules (p+(-q) follows number line: start at p, move |q| left); contexts like money $10 spend $25 (10-25=-15, debt). Mistakes include context misapplied (debt shown as positive balance), or not rewriting as addition (missing p-q=p+(-q)).

This question tests understanding that subtraction p - q equals adding the additive inverse p + (-q), and the distance between numbers as |p - q| (absolute value of the difference). Subtraction as addition: p - q = p + (-q) by definition (subtracting q means adding the opposite -q: 5 - 8 = 5 + (-8) = -3, or 7 - (-3) = 7 + 3 = 10 since subtracting a negative adds the positive). On the number line, p - q starts at p and moves |q| units left if q > 0 (subtracting a positive) or right if q < 0 (subtracting a negative equals adding a positive), while the distance between p and q is |p - q| = |q - p| (absolute value of the difference, always positive: |3 - 10| = |-7| = 7 units apart, or |10 - 3| = 7). For example, 15 - 20 can be rewritten as 15 + (-20) = -5 (like a temperature drop from 15°C to -5°C), or the distance from -4 to 3 is |3 - (-4)| = |3 + 4| = 7 units (or |-4 - 3| = |-7| = 7), and for money, 10 - 25 = 10 + (-25) = -15 (a debt of $15). The correct equation is 5 - (-2) = 5 + 2 = 7, as it shows subtracting a negative becomes adding a positive. A common error is subtracting negative wrong, like in choice A where 5 - (-2) = 5 + (-2) = 3 treats it as adding negative, or in choice B where it stays as 5 - 2 = 3 without converting. Using the additive inverse, rewrite every subtraction as addition (p - q → p + (-q), making all operations additions), and apply addition rules (p + (-q) follows number line interpretation: start at p, move |q| left).

This question tests understanding that subtraction p-q equals adding the additive inverse p+(-q), and the distance between numbers as |p-q| (absolute value of the difference). Subtraction as addition: p-q = p+(-q) by definition (subtracting q means adding the opposite -q: 5-8=5+(-8)=-3, or 7-(-3)=7+3=10 subtracting negative adds positive). Number line: p-q starts at p, moves distance |q| left if q>0 (subtracting positive), or right if q<0 (subtracting negative = adding positive). Distance between p and q: |p-q|=|q-p| (absolute value of difference, always positive: |3-10|=|-7|=7 units apart, or |10-3|=7). The distance between -4 and 3 is |-4-3|=|-7|=7, matching choice A. A common error is choosing B (-4-3=-7), which gives a negative without absolute value, or C (|3-(-4)|=-7), which incorrectly assigns a negative to the absolute value. Distance: between any two numbers p and q, calculate p-q, take absolute value |p-q| (removes sign, gives positive distance: 3-10=-7, |-7|=7 units), or reverse: |q-p| (order doesn't matter for distance, both give same). Mistakes: not rewriting as addition (missing connection p-q=p+(-q)), subtracting negative as subtraction (5-(-2) staying as subtract when should become 5+2=7), distance without absolute value (negative distance).

This question tests understanding that subtraction p-q equals adding the additive inverse p+(-q), and the distance between numbers as |p-q| (absolute value of the difference). Subtraction as addition: p-q = p+(-q) by definition (subtracting q means adding the opposite -q: 5-8=5+(-8)=-3, or 7-(-3)=7+3=10 since subtracting a negative adds the positive). On the number line, p-q starts at p and moves distance |q| left if q>0 (subtracting positive), or right if q<0 (subtracting negative = adding positive); distance between p and q is |p-q|=|q-p| (absolute value of the difference, always positive: |3-10|=|-7|=7 units apart, or |10-3|=7). For example, 15-20 can be rewritten as 15+(-20)=-5 (temperature drops from 15°C to -5°C), or distance from -4 to 3: |3-(-4)|=|3+4|=7 units (or |-4-3|=|-7|=7), or 10-25 for money: 10+(-25)=-15 (debt of $15). The correct expression is |3-10|=|-7|=7, so distance 7, as in choice C, using absolute value properly. A common error is distance negative, like choice A |10-3|=-7 (wrong absolute), or choice B 10-3=7 without absolute value (works but not general), or choice D |10-3|=|13|=13 (arithmetic error). Distance: calculate p-q, take |p-q| (positive: 3-10=-7, |-7|=7), or |q-p| (same); mistakes include distance without absolute value (negative distance), or wrong order.

This question tests understanding that subtraction p-q equals adding the additive inverse p+(-q), and the distance between numbers as |p-q| (absolute value of the difference). Subtraction as addition: p-q = p+(-q) by definition (subtracting q means adding the opposite -q: 5-8=5+(-8)=-3, or 7-(-3)=7+3=10 since subtracting a negative adds the positive). On the number line, p-q starts at p and moves distance |q| left if q>0 (subtracting positive), or right if q<0 (subtracting negative = adding positive); distance between p and q is |p-q|=|q-p| (absolute value of the difference, always positive: |3-10|=|-7|=7 units apart, or |10-3|=7). For example, 15-20 can be rewritten as 15+(-20)=-5 (temperature drops from 15°C to -5°C), or distance from -4 to 3: |3-(-4)|=|3+4|=7 units (or |-4-3|=|-7|=7), or 10-25 for money: 10+(-25)=-15 (debt of $15). The claim is false because -2-5=-7 and -2+(-5)=-7 (same), as in choice C, confirming equivalence. A common error is claiming p-q≠p+(-q) with wrong calculations, like choice A with -2+(-5)=7 (sign error), or choice B with -2-5=-3 (arithmetic wrong), or choice D with both as 3 (multiple errors). Using additive inverse: rewrite p-q→p+(-q), apply addition (start p, move left); mistakes like denying equivalence (p-q≠p+(-q) claimed), or subtracting negative wrong (5-(-2)=3 not 7).

This question tests understanding that subtraction p - q equals adding the additive inverse p + (-q), and the distance between numbers as |p - q| (absolute value of the difference). Subtraction as addition: p - q = p + (-q) by definition (subtracting q means adding the opposite -q: 5 - 8 = 5 + (-8) = -3, or 7 - (-3) = 7 + 3 = 10 since subtracting a negative adds the positive). On the number line, p - q starts at p and moves |q| units left if q > 0 (subtracting a positive) or right if q < 0 (subtracting a negative equals adding a positive), while the distance between p and q is |p - q| = |q - p| (absolute value of the difference, always positive: |3 - 10| = |-7| = 7 units apart, or |10 - 3| = 7). For example, 15 - 20 can be rewritten as 15 + (-20) = -5 (like a temperature drop from 15°C to -5°C), or the distance from -4 to 3 is |3 - (-4)| = |3 + 4| = 7 units (or |-4 - 3| = |-7| = 7), and for money, 10 - 25 = 10 + (-25) = -15 (a debt of $15). The correct statement is that Student 1 is right, and Student 2 should have |3 - 10| = |-7| = 7, as distance uses absolute value and is always positive regardless of order. A common error is claiming distance can be negative, like in choice A where Student 2 is correct with -7, or in choice D where both are correct with negative distance. Distance: between any two numbers p and q, calculate p - q and take the absolute value |p - q| (removes the sign, gives positive distance: 3 - 10 = -7, |-7| = 7 units), or reverse |q - p| (order doesn't matter for distance, both give the same).

This question tests understanding that subtraction p-q equals adding the additive inverse p+(-q), and the distance between numbers as |p-q| (absolute value of the difference). Subtraction as addition: p-q = p+(-q) by definition (subtracting q means adding the opposite -q: 5-8=5+(-8)=-3, or 7-(-3)=7+3=10 since subtracting a negative adds the positive). On the number line, p-q starts at p and moves distance |q| left if q>0 (subtracting positive), or right if q<0 (subtracting negative = adding positive); distance between p and q is |p-q|=|q-p| (absolute value of the difference, always positive: |3-10|=|-7|=7 units apart, or |10-3|=7). For example, 15-20 can be rewritten as 15+(-20)=-5 (temperature drops from 15°C to -5°C), or distance from -4 to 3: |3-(-4)|=|3+4|=7 units (or |-4-3|=|-7|=7), or 10-25 for money: 10+(-25)=-15 (debt of $15). The correct modeling for 15-20 is 15+(-20)=-5°C, as in choice B, rewriting subtraction as addition for the temperature drop. A common error is arithmetic wrong, like choice A as 15+20=35°C (adding instead of subtracting), or choice C with sum as 5°C (absolute value error), or choice D subtracting -20 which adds 20 incorrectly. Contexts: temperature 15° drops 20° (15-20=-5°, below zero), money $10 spend $25 (10-25=-15, debt), elevation 50 m descend 80 m (50-80=-30 m, below sea level 30 m); using additive inverse rewrites to addition for easier calculation.

This question tests understanding that subtraction p - q equals adding the additive inverse p + (-q), and the distance between numbers as |p - q| (absolute value of the difference). Subtraction as addition: p - q = p + (-q) by definition (subtracting q means adding the opposite -q: 5 - 8 = 5 + (-8) = -3, or 7 - (-3) = 7 + 3 = 10 since subtracting a negative adds the positive). On the number line, p - q starts at p and moves |q| units left if q > 0 (subtracting a positive) or right if q < 0 (subtracting a negative equals adding a positive), while the distance between p and q is |p - q| = |q - p| (absolute value of the difference, always positive: |3 - 10| = |-7| = 7 units apart, or |10 - 3| = 7). For example, 15 - 20 can be rewritten as 15 + (-20) = -5 (like a temperature drop from 15°C to -5°C), or the distance from -4 to 3 is |3 - (-4)| = |3 + 4| = 7 units (or |-4 - 3| = |-7| = 7), and for money, 10 - 25 = 10 + (-25) = -15 (a debt of $15). The correct expression is -3/2 - 5/2 = -8/2 = -4, as it computes the new elevation after descending. A common error is rewriting incorrectly, like in choice A where -3/2 - 5/2 = -3/2 + 5/2 = 1 adds instead of subtracting, or in choice C where it becomes positive 4 without proper signs. Mistakes: not rewriting as addition (missing connection p - q = p + (-q)), subtracting negative as subtraction (5 - (-2) staying as subtract when should become 5 + 2 = 7), distance without absolute value (negative distance).

This question tests understanding that subtraction p-q equals adding the additive inverse p+(-q), and the distance between numbers as |p-q| (absolute value of the difference). Subtraction as addition: p-q = p+(-q) by definition (subtracting q means adding the opposite -q: 5-8=5+(-8)=-3, or 7-(-3)=7+3=10 subtracting negative adds positive). Number line: p-q starts at p, moves distance |q| left if q>0 (subtracting positive), or right if q<0 (subtracting negative = adding positive). Distance between p and q: |p-q|=|q-p| (absolute value of difference, always positive: |3-10|=|-7|=7 units apart, or |10-3|=7). For -9-(-4), rewrite as -9+4=-5, matching choice C. A common error is choosing A (-13), which subtracts instead of adding, or B (13), which ignores signs. Using the additive inverse: rewrite every subtraction as addition (p-q→p+(-q), makes all operations additions), apply addition rules (p+(-q) follows number line interpretation: start p, move |q| left). Contexts: temperature 15° drops 20° (15-20=-5°, below zero), money $10 spend $25 (10-25=-15, debt), elevation 50 m descend 80 m (50-80=-30 m, below sea level 30 m).

This question tests understanding that subtraction p - q equals adding the additive inverse p + (-q), and the distance between numbers as |p - q| (absolute value of the difference). Subtraction as addition: p - q = p + (-q) by definition (subtracting q means adding the opposite -q: 5 - 8 = 5 + (-8) = -3, or 7 - (-3) = 7 + 3 = 10 since subtracting a negative adds the positive). On the number line, p - q starts at p and moves |q| units left if q > 0 (subtracting a positive) or right if q < 0 (subtracting a negative equals adding a positive), while the distance between p and q is |p - q| = |q - p| (absolute value of the difference, always positive: |3 - 10| = |-7| = 7 units apart, or |10 - 3| = 7). For example, 15 - 20 can be rewritten as 15 + (-20) = -5 (like a temperature drop from 15°C to -5°C), or the distance from -4 to 3 is |3 - (-4)| = |3 + 4| = 7 units (or |-4 - 3| = |-7| = 7), and for money, 10 - 25 = 10 + (-25) = -15 (a debt of $15). The correct distance is |3 - (-4)| = |7| = 7, as it applies the absolute value to the difference properly. A common error is treating distance as negative without absolute value, like in choice A where |-4 - 3| = |-7| = -7 claims a negative distance, or in choice C where 3 - (-4) = -1 miscalculates the subtraction. Distance: between any two numbers p and q, calculate p - q and take the absolute value |p - q| (removes the sign, gives positive distance: 3 - 10 = -7, |-7| = 7 units), or reverse |q - p| (order doesn't matter for distance, both give the same).