12 (a) Multiply out - OCR - GCSE Maths - Question 12 - 2018 - Paper 1

To multiply out the expression $(3x + 2)(x - 4)$, we apply the distributive property:

1. First, multiply $3x$ by both terms in $(x - 4)$:

   • $3x imes x = 3x^2$
   • $3x imes -4 = -12x$

2. Next, multiply $2$ by both terms in $(x - 4)$:

   • $2 imes x = 2x$
   • $2 imes -4 = -8$

3. Now combine all the terms: $3x^2 - 12x + 2x - 8$

4. Combine like terms: $3x^2 - 10x - 8$.

To solve the inequality $3x - 2 o 22$, we first isolate $x$:

1. Add $2$ to both sides: $3x o 24$

2. Divide both sides by $3$: $x o 8$

Thus, the solution to the inequality is: $x ≤ 8$.