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Standard VIII

Mathematics

Word Problems in Multiplication and Division

Solve the fol...

Question

Solve the following equations:
a) $5 (3 - x) - 2 (4 - 3 x) = 11 - 2 (x - 1)$
b) $6 - 4 (x + 3) = 2 (x - 1)$
c) $5 (1 - 2 x) + 2 (3 - x) = 3 (x + 4) + 14$

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Solution

a)
$5 (3 - x) - 2 (4 - 3 x) = 11 - 2 (x - 1)$
$15 - 5 x - 8 + 6 x = 11 - 2 x + 2$
$7 + x = 13 - 2 x$
$x + 2 x = 13 - 7$
$3 x = 6$
$x = 2$
b)
$6 - 4 (x + 3) = 2 (x - 1)$
$6 - 4 x - 12 = 2 x - 2$
$- 4 x - 6 = 2 x - 2$
$- 4 x - 2 x = - 2 + 6$
$- 6 x = 4$
$x = \frac{- 4}{6}$
$x = - 2 / 3$
c)
$5 (1 - 2 x) + 2 (3 - x) = 3 (x + 4) + 14$
$5 - 10 x + 6 - 2 x = 3 x + 12 + 14$
$- 12 x + 11 = 3 x + 26$
$- 12 x - 3 x = 26 - 11$
$- 15 x = 15$
$x = - 1$

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Similar questions

Solve the equations:

(i) 5x = 3x + 24;

(ii) 8t + 5 = 2t − 31;

(iii) 7x − 10 = 4x + 11;

(iv) 4z + 3 = 6 + 2z;

(v) 2x − 1 = 14 − x;

(vi) 6x + 1 = 3(x − 1) + 7;

(vii) ;

(viii) ;

(ix) 3(x + 1) = 12 + 4 (x − 1);

(x) 2x − 5 = 3(x − 5);

(xi) 6(1 − 4x) + 7(2 + 5x) = 53;

(xii) 3(x + 6) + 2 (x + 3) = 64;

(xiii) ;

(xiv) .

Q. Solve the following equations:
(a)

x - 5 = 7

(b)

3 x + 18 = 48

(c)

2 x = 48

(d)

5 (x - 1) + 3 = 23

Solve :

$(i) \frac{1}{3} x - 6 = \frac{5}{2} (i i) \frac{2 x}{3} - \frac{3 x}{8} = \frac{7}{12} (i i i) (x + 2) (x + 3) + (x - 3) (x - 2) - 2 x (x + 1) = 0 (i v) \frac{1}{10} - \frac{7}{x} = 35 (v) 13 (x - 4) - 3 (x - 9) - 4 (x + 4) = 0 (v i) x + 7 - \frac{8 x}{3} = \frac{17 x}{6} - \frac{5 x}{8} (v i i) \frac{3 x - 2}{4} - \frac{2 x + 3}{3} = \frac{2}{3} - x (v i i i) \frac{x + 2}{6} - (\frac{11 - x}{3} - \frac{1}{4}) = \frac{3 x - 4}{12} (i x) \frac{2}{5 x} - \frac{5}{3 x} = \frac{1}{15} (x) \frac{x + 2}{3} - \frac{x + 1}{5} = \frac{x - 3}{4} - 1 (x i) \frac{3 x - 2}{3} + \frac{2 x + 3}{2} = x + \frac{7}{6} (x i i) x - \frac{x - 1}{2} = 1 - \frac{x - 2}{3} (x i i i) \frac{9 x + 7}{2} - (x - \frac{x - 2}{7}) = 36 (x i v) \frac{6 x + 1}{2} + 1 = \frac{7 x - 3}{3}$

Q. Solve for

x

\frac{(3 x + 1)}{6} + \frac{(2 x - 3)}{7} = \frac{(x + 3)}{8} + \frac{(3 x - 1)}{14}

Solve the following equations:

$(i) 3^{x + 1} = 27 \times 3^{4} (i i) 4^{2 x} = (\sqrt[3]{16})^{\frac{- 6}{y}} = (\sqrt{8})^{2} (i i i) 3^{x - 1} \times 5^{2 y - 3} = 225 (i v) 8^{x + 1} = 16^{y + 2} a n d {(\frac{1}{2})}^{3 + x} = {(\frac{1}{4})}^{3 y} (v) 4^{x - 1} \times (0.5)^{3 - 2 x} = {(\frac{1}{8})}^{x} (v i) \sqrt{\frac{a}{b}} = {(\frac{b}{a})}^{1 - 2 x}, w h e r e a, b a r e d i s t i n c t p o s i t i v e p r i m e s .$

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Solve the following equations:a) 5(3−x)−2(4−3x)=11−2(x−1)b) 6−4(x+3)=2(x−1)c) 5(1−2x)+2(3−x)=3(x+4)+14

a) 5(3−x)−2(4−3x)=11−2(x−1)15−5x−8+6x=11−2x+27+x=13−2xx+2x=13−73x=6x=2b)6−4(x+3)=2(x−1)6−4x−12=2x−2−4x−6=2x−2−4x−2x=−2+6−6x=4x=−46x=−2/3c)5(1−2x)+2(3−x)=3(x+4)+145−10x+6−2x=3x+12+14−12x+11=3x+26−12x−3x=26−11−15x=15x=−1

Solve the following equations:
a) $5 (3 - x) - 2 (4 - 3 x) = 11 - 2 (x - 1)$
b) $6 - 4 (x + 3) = 2 (x - 1)$
c) $5 (1 - 2 x) + 2 (3 - x) = 3 (x + 4) + 14$