Solving inequalities questions with answers

Questions

1. Question 1ax + b > c

   Solve $2x + 9 \leq -9$.

   Show the worked solution

   1. Step 1: Collect the x terms on one side and the numbers on the other$2x \leq -18$
   2. Step 2: Divide both sides by the number in front of x. Does the sign change?$x \leq -9$
2. Question 2Negative x term

   Solve $9 - 2x \geq -9$.

   Show the worked solution

   1. Step 1: Collect the x terms on one side and the numbers on the other$-2x \geq -18$
   2. Step 2: Divide both sides by the number in front of x. Does the sign change?$x \leq 9$ (dividing by a negative number reverses the sign)
3. Question 3x on both sides

   Solve $5x + 2 \leq 2x - 3$.

   Show the worked solution

   1. Step 1: Collect the x terms on one side and the numbers on the other$3x \leq -5$
   2. Step 2: Divide both sides by the number in front of x. Does the sign change?$x \leq -\dfrac{5}{3}$
4. Question 4Fractions

   Solve $\dfrac{2x + 2}{4} < \dfrac{3x + 3}{3}$.

   Show the worked solution

   1. Step 1: Multiply both sides by the LCM of the denominators$3(2x + 2) < 4(3x + 3)$
   2. Step 2: Expand the brackets$6x + 6 < 12x + 12$
   3. Step 3: Collect the x terms on one side and the numbers on the other$-6x < 6$
   4. Step 4: Divide both sides by the number in front of x. Does the sign change?$x > -1$ (dividing by a negative number reverses the sign)