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Solving onestep equations and inequalitiesIn solving onestep equations and inequalities, the student should know all the rules of inequality. For this you can refer the previous page of askmath or visit the link given below.Rules for solving linear equations inequalities Steps involved while solving onestep equations and inequalities1) Isolate the given variable. For this use the opposite operation rule.(i)Addition > Subtraction (ii)Subtraction > Addition (iii)Multiplication > Division (iv)Division > Multiplication. 2) If you are dividing or multiply both the sides by negative number then flip the sign. (i)greater than (>) becomes less than (<) (ii)less than (<) becomes greater than (>) (iii)greater than and equal to ($\geq$) becomes less than and equal to ($\leq$) (iv)less than and equal to ($\leq$) becomes greater than and equal to ($\geq$) Example 1 : x + 8 > 11 Solution : x + 8 > 11 Since there is positive 8 so as to isolate x, we will add negative(8) on both sides x + 8  8 > 11  8 ∴ x > 3 ( + 8  8 = 0) Example 2 : x  11 < 5 Solution : x  11 < 5 Since there is negative 11 so as to isolate x, we will add positive 11 (+11) on both sides x  11 + 11 < 5 + 11 ∴ x < 16  (  11 + 11 = 0) Example 3 : x + 72 $\geq$ 65 Solution : x + 72 $\geq$ 65 Since there is positive 72 so as to isolate x, we will add negative 72 (72) on both sides x + 72  72 $\geq$ 65  72 ∴ x $\geq$ 7  ( 72  72 = 0) Example 4 : 5x $\leq$ 65 Solution : 5x $\leq$ 65 Since there is multiplication between 5 and x so to isolate x, we will divide both side by 5 $\frac{5x}{5}$ $\leq$ $\frac{65}{5}$ ∴ x $\leq$ 13  ( 5 ÷ 5 = 1) Example 5 : $\frac{x}{8}$ $\geq$ 6 Solution : $\frac{x}{8}$ $\geq$ 6 Since there is division between x and 8 so to isolate x, we will multiply both side by 8 $\frac{x}{8}\times 8$ $\geq$ 8 $\times$ 6 ∴ x $\geq$ 48  ( 8 ÷ 8 = 1) Example 6 : 12x $\leq$ 48 Solution : 12x $\leq$ 48 Since there is multiplication between negative 12 (12) and x so to isolate x, we will divide both side by (12) $\frac{12x}{12}$ $\leq$ $\frac{48}{12}$ According to inequality rule, we have to flip the inequality sign. ∴ x $\geq$ 4 ( 12 ÷ 12 =+1 and 48 ÷ (12)= 4 ) Example 7 : $\frac{x}{5}$ $\geq$  11 Solution : $\frac{x}{5}$ $\geq$  11 Since there is division between x and (5) so to isolate x, we will multiply both side by (5) $\frac{x}{5}\times (5)$ $\geq$ 11 $\times$ (5) According to inequality rule, we have to flip the inequality sign. ∴ x $\leq$ 55  ( (5) ÷ (5) = 1 and (11) X (5) = +55 From solving one step inequality to Home
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