Rules for solving Inequations

Rules for Solving a Linear Inequality

<, >, ≤ and ≥ are known as signs or an inequality.

Rule 1

If a positive number is added to both sides of an inequality, the sign of inequality remains the same.

(a) x+3<5 => x + 3 + 2 < 5 + 2

(b) x+1>3 => x + 1 + 1 > 3 + 1

(c) x+3≥7 =>  x + 3 + 1≥7 +1

(d) x+5≤9 => x + 5 + 2 <= 9 + 2

Rule 2:-

If a negative number is subtracted on both sides of an inequality, the sign of that  ineq -uality remains the same.

(a) x+1<5 => x+1-2< 5-2

(b) x+3>7 => x+3-2>7-2

(c) x + 2≼ 11 =>x+2-1≼ 11-1

(d) x + 5≥9 => x+5-2 ≥ 9-2

Rule 3:- 

If we multiply the both sides of an inequality with the same positive number, then the sign of the inequality remains the same.

(a) x < 2 => x×5<2×5 

(b) x > 5 => x×2>5×2

(c)x ≤ 3 => x× 2 ≤ 2×3

(d) x ≤7 => x ×3≤ 7×3

Rule 4 :-

If we multiply both sides of an inequality with the same negative number, then the inequality will reverse i.e. the sign of inequality reversed.

(a) x < 5 => (-2)× x > (-2)×5

(b) x > 4 =>  (-3) × x < (-3) × 4 

(c) x ≤ 9 => (-1) × x ≥ (-1) × 9 

(d) x≽3 => (-2)×x ≼ (-2)×3

Rule 5:- 

If both sides of an inequality are divided by the same positive number, then the sign of inequality remains the same.

(a) x<5  => x/2 < 5/2

(b)x>3 => x/3 > 3/3

(c) x ≤2  =>   x/2 ≤  2/2

(d) x≥6 => x/3 ≥6/3

Rule 6 :-

If both the sided of an inequality are divided by same negative number, then the sigh of inequality will reverse. 

(a) x<4 => x/(-2) > 4/(-2)

(b) x>5 => x/(-3) < 5/(-3)

(c) x≤6 => x/(-2) ≥ 6/(-2)

(d) x≥8 => x/(-4)≤ 8/(-4)