Question

Solve: $2.4(3-x)-0.6(2x-3)=0$

Answer 1

We have: $2.4(3-x)-0.6(2x-3)=0$

$\Rightarrow 10\times 2.4(3-x)-10\times 0.6(2x-3)=0$ (Multiplying both sides by $10$ to remove decimals)

$\Rightarrow 24(3-x)-6(2x-3)=0$

$\Rightarrow 6\left[4\right(3-x)-(2x-3\left)\right]=0$ [Takin $6$ common]

$\Rightarrow 4(3-x)-(2x-3)=0$

$\Rightarrow 12-4x-2x+3=0$

$\Rightarrow 15-6x=0$

$\Rightarrow -6x=-15$

$\Rightarrow x=\frac{15}{6}$

$\Rightarrow x=\frac{5}{2}=2.5$

CHECK: Substituting $x=2.5$ in the given equation, we get:

LHS $=2.4(3-x)-0.6(2x-3)$

$=2.4(3-2.5)-0.6(2\times 2.5-3)=2.4\times 0.5-0.6\times 2=1.2-1.2=0$

RHS $=0$

$\therefore$ LHS $=$ RHS

Hence, $x=\frac{5}{2}=2.5$ is a solution of the given equation.