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Standard VIII

Mathematics

Solving Equations with Linear Expressions on One Side and Numbers on the Other Side

Solve the fol...

Question

Solve the following equations :

$(x - 1) (x + 6) - (x - 2) (x - 3) = 3$

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Solution

$(x - 1) (x + 6) - (x - 2) (x - 3) = 3 x^{2} - x + 6 x - 6 - (x^{2} - 3 x - 2 x + 6) = 3 \Rightarrow x^{2} - x + 6 x - 6 - (x^{2} + 3 x + 2 x - 6) = 3 \Rightarrow - x + 6 x + 3 x + 2 x - 6 - 6 = 3 - x + 11 x - 6 - 6 = 3 10 x = 15 x = \frac{15}{10} = \frac{3}{2} = 1 \frac{1}{2}$

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Similar questions

Q. Solve:

(x - 1) (x + 6) - (x - 2) (x - 3) = 3

Q. Solve the following inequality:

\frac{(x - 1) (x - 2) (x - 3)}{(x + 1) (x + 2) (x + 3)} > 1

Solve the following quadratic equation by factorization.
$\frac{1}{(x - 1) (x - 2)} + \frac{1}{(x - 2) (x - 3)} + \frac{1}{(x - 3) (x - 4)} = \frac{1}{6}$

Q. Solve the following equation by using properties of determinants

∣ ∣ ∣ ∣ \begin{matrix} x + 2 x + 6 x - 1 \end{matrix} \begin{matrix} x + 6 x - 1 x + 2 \end{matrix} \begin{matrix} x - 1 x + 2 x + 6 \end{matrix} ∣ ∣ ∣ ∣ = 0

Q. Solve:

\frac{(x - 1) (x - 2) (x - 3)}{(x + 1) (x + 2) (x + 3)} > 1

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Solve the following equations : (x−1)(x+6)−(x−2)(x−3)=3

(x−1)(x+6)−(x−2)(x−3)=3x2−x+6x−6−(x2−3x−2x+6)=3⇒ x2−x+6x−6−(x2+3x+2x−6)=3⇒ −x+6x+3x+2x−6−6=3−x+11x−6−6=310x=15x=1510=32=112

Solve the following equations :

$(x - 1) (x + 6) - (x - 2) (x - 3) = 3$

$(x - 1) (x + 6) - (x - 2) (x - 3) = 3 x^{2} - x + 6 x - 6 - (x^{2} - 3 x - 2 x + 6) = 3 \Rightarrow x^{2} - x + 6 x - 6 - (x^{2} + 3 x + 2 x - 6) = 3 \Rightarrow - x + 6 x + 3 x + 2 x - 6 - 6 = 3 - x + 11 x - 6 - 6 = 3 10 x = 15 x = \frac{15}{10} = \frac{3}{2} = 1 \frac{1}{2}$