# A solution is to be kept between $68^{\circ} F$ and $77^{\circ} F$ . What is the range in to temperature in degree ceisius (C) if the ceisius (C) if the ceisius / Fahrenheit (F) conversion. formula is given by $F= \large\frac{9}{8} $$c +32? ## 1 Answer Toolbox: • Same Quantity can be added (a subtracted ) to (from ) both sides of the inequality with out changing the sign of the in equality. • Same positive quantities can be multiplied or divided to both side of the in equality with out changing the sign of the inequality. • If same negative quantity is multiplied or divided to both sides of the inequality is reversed i.e '>' sign changes to '<' and '<' changes '>' . Step 1: Since the solution is to be kept between 68^{\circ} and 77^{\circ} F We have that, 68 < F <77 Substituting for F= \large\frac{9}{5}$$C +32$
We get $68 < \large\frac{9}{5}$$c +32 < 77 Step 2: Subtracting 32 from both sides of inequality => 68-32 < \large\frac{9}{5}$$ C < 77 -32$
$=> 36 < \large\frac{9}{5} $$C<45 Multiplying by positive number \large\frac{5}{9} on both sides, of inequality => 36 \times \large\frac{5}{9} < \frac{9}{5} \times \frac{5}{9}$$C < 45 \times \large\frac{5}{9}$
$=> 20 < C <25$
Step 3:
The required range of temperature in degree ceisius is between $20^{\circ}$ and $25^{\circ}C$