Distributing
1. 6(x + 2) + 4(x + 3) = 10x + 24, which is what was written — this line is correct2. 4(x + 3) + 5(x + 7) = 9x + 47, not 5x + 19 (the second bracket was never multiplied out)3. 6(x + 7) + 3(x + 7) = 9x + 63, which is what was written — this line is correct4. 4(x + 7) + 6(x + 8) = 10x + 76, not 10x + 1344 (the two numbers were multiplied together where they should be added)5. 5(x + 7) + 4(x + 2) = 9x + 43, which is what was written — this line is correctSigns and dividing
1. (5x + 30) ÷ 5 − (x + 3) = 3, not 9 (the minus reached the x in the second bracket but not the number)2. 7(x + 7) − (x − 7) = 6x + 56, not 6x + 42 (the minus reached the x in the second bracket but not the number)3. (2x + 10) ÷ 2 − (x + 4) = 1, not x + 1 (the two x terms were never cancelled against each other)4. 4(x + 8) − (x − 5) = 3x + 37, not 3x + 27 (the minus reached the x in the second bracket but not the number)5. 7(x + 5) − (x − 7) = 6x + 42, which is what was written — this line is correctExponent laws
1. (x⁴)² · x³ = x¹¹, not x²⁴ (the last power was multiplied in as well as the first two)2. (x⁴)⁴ · x² = x¹⁸, not x³² (the last power was multiplied in as well as the first two)3. (x²)⁴ · x³ = x¹¹, not x⁹ (the stacked powers were added where they should be multiplied)4. x⁴ · x⁴ ÷ x² = x⁶, not x² (the second power was taken away and the third one added)5. x³ · x³ ÷ x⁴ = x², not x⁴ (the second power was taken away and the third one added)
