Question

four times a number is less than or equal to half the sum of a number and -2

Answer 1

Let x be the unknown number.

1. Four times a number x is 4·x=4x;
2. Half the sum of a number x and -2 is $\dfrac{x+(-2)}{2}=\dfrac{x-2}{2}.$

Then the inequality will have form:

$4x\le \dfrac{x-2}{2}.$

Solve it. First, multiply this inequality by 2:

$2\cdot 4x\le 2\cdot \dfrac{x-2}{2},\\ \\8x\le x-2.$

Then separate terms with x in left side and without x in right side:

$8x-x\le -2,\\ \\7x\le -2.$

and divide it by 7:

$x\le -\dfrac{2}{7}.$

Answer: $x\le -\dfrac{2}{7}.$