The real x for which $2(2x + 3) - 10 < 6 (x - 2)$ is :

Step 1: Expand both sides of the inequality

First, we distribute the numbers outside the parentheses to the terms inside on both sides of the inequality. On the left side, $2 \times 2x = 4x$ and $2 \times 3 = 6$. On the right side, $6 \times x = 6x$ and $6 \times -2 = -12$.

Step 2: Simplify both sides

Next, we combine the constant terms on the left side of the inequality. $6 - 10$ simplifies to $-4$. The right side remains $6x - 12$.

Step 3: Collect x terms on one side

To isolate the variable $x$, we move all terms containing $x$ to one side and constant terms to the other. Subtract $6x$ from both sides and add $4$ to both sides.

Step 4: Simplify and solve for x

Combine the terms: $4x - 6x = -2x$ and $-12 + 4 = -8$. Finally, divide both sides by $-2$. Remember to reverse the inequality sign when dividing by a negative number.

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