Learn – Algebra foundations – Inequalities

Problem set 1

What does $y = x + 5$ represent on XY-plane?
What does $y > x + 5$ represent on XY-plane?
What does $y < x + 5$ represent on XY-plane?

Problem set 2
Plot the following on the $XY$ -plane.

$3y - 2x \ge 2y + x + 5$
$x > 2y + 3x + 5$
$x \le 2y + x + 5$
$3y + 2x - y < 2y + x + 5$

Problem set 3
Plot the following on the $XY$ -plane.

$y = x^2$
$y < x^2$
$xy = 1$
$xy < 1$

Problem set 4

Show $y$ on number line: $-10y \le 30$
Show $x$ on number line: $8 - 7x \le -20$
Show $x$ on number line: $2x + 5 < -7x -12$
Show $x$ on number line: $2 < 7x - 5 < 23$
Solve simultaneously: $x$ is an integer, $x^2 + 4x - 7 < x^2 + 2x + 1$ and $2 - 3x < -4$ .

Problem set 5

Show $x$ on number line: $2 < -7x - 5 < 23$
Show $y$ on number line: $x^2 < 4$
Show $x$ on number line: $2x^3 \ge 54$
Show $x$ on number line: $16 < 2x^3 \le 54$
Solve simultaneously: $x$ is an integer, $2x^2 + 4x - 7 > 2x^2 + 2x + 1$ and $4 - 3x > -11$ .

Problem set 6

Show $x$ on number line: $2x^3 \ge 0.054$
Show $x$ on number line: $-0.016 \le 2x^3 < 0.054$
Show $x$ on number line: $x > 0$ and $x \le \sqrt{x}$
Show $x$ on number line: $x^2 > x$
Show $x$ on number line: $x^2+2x-6 > x^2-3x+6$

Problem set 7

Show $x$ on number line: $x^2 \le x$
Show $x$ on number line: $x^2 < |x|$
Show $x$ on number line: $x > 0$ and $x^{99} < x^9$
Show $x$ on number line: $x^2 > x^3$
Show $x$ on number line: $2x^2+2x-6 > x^2+2x+10$