User:Atcovi/SolvingInequalitiesNumber7

$$9 + x < 7 - 2(x-3)$$ Distribute $$9 + x < 7 - 2x + 6$$ Combine like terms (7 and 6) LEFT DISTRIBUTIVE PROPERTY OF EQUALITY $$9 + x < -2x + 13$$ 2x becomes negative due to the subtraction sign from the 2nd step of the problem. We get the number 13 from 7 and 6. ADDITIVE PROPERTY OF EQUALITY $$9 + 3x < 0x + 13$$ We add 2x to both sides, allowing us to cancel -2x and getting 3x (x(x is 1) + 2x = 3x) ADDITIVE INVERSE $$9(-9) + 3x < 13(-9)$$ Minus nine from both sides ADDITIVE IDENTITY $$3x < 4$$ We simply divide all of this by 3 SUBTRACTION PROPERTY OF EQUALITY $$\tfrac{3x}{3}$$ < $$\tfrac{4}{3}$$ This execution results in cancelling out the 3 in 3x and dividing 4 by 3, which results in: DIVISION PROPERTY OF EQUALITY $$1x < 1.333$$ We do not want decimals, so convert it to a fraction: IDENTITY PROPERTY OF MULTIPLICATION $$x < 4/3$$

So, basically, x is less than 4/3.

CONFIRMATION