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

First, we will multiply the expressions:

$(3x + 2)(x - 4)$

Applying the distributive property:

1. Multiply $3x$ by both terms in $(x - 4)$:

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

2. Multiply $2$ by both terms in $(x - 4)$:

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

Combining all terms, we get:

$3x^2 - 12x + 2x - 8$

Now, simplify the $x$ terms:

$3x^2 - 10x - 8$

To solve the inequality $3x - 2 ≤ 22$, follow these steps:

1. Add $2$ to both sides of the inequality: $3x ≤ 24$

2. Divide both sides by $3$: $x ≤ 8$

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