(1) 2x − 5 = 1
(2) 3x − 2 = −7
(3) 4x + 7 = 15

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Solution

(1) 2x − 5 = 1
⇒ 2x = 6
⇒ x = 6 ÷ 2
∴ x = 3

(2) 3x − 2 = −7
⇒ 3x = −5
⇒ x = $\frac{- 5}{3}$
∴ x = $\frac{- 5}{3}$

(3) 4x + 7 = 15
⇒ 4x = 8
⇒ x = $\frac{8}{4}$
∴ x = 2

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Similar questions

Q. Find x

\frac{(4 x + 1)}{3} + \frac{(2 x - 1)}{2} - \frac{(3 x - 7)}{5} = 6

Q. Match the equations in List 1 with the solutions in List 2

	List I		List II
A.	${log}_{0.25} {(x^{2} + 2 x - 8)}^{2}$ $- {log}_{0.5} (10 + 3 x - x^{2}) = 1$	1.	${- 3}$
B.	${log}_{2} (x^{2} + 7)$ $= 5 + {log}_{2} x$ $- \frac{6}{{log}_{2} (x + \frac{7}{x})}$	2.	${\frac{1}{4}}$
C.	${log}_{(1 - 2 x)} (6 x^{2} - 5 x + 1)$ $- {log}_{(1 - 3 x)} (4 x^{2} - 4 x + 1) = 2$	3.	${\frac{1}{6} (\sqrt{313} - 1), \frac{1}{2} (\sqrt{73} - 7)}$
D.	${log}_{10} (1 {+ x}^{2} - 2 x) + 1 - {log}_{10} (1 + x^{2}) =$ $2 {log}_{10} (1 - x)$	4.	${1, 7}$

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:

\frac{3 x + 2}{7} + \frac{4 (x + 1)}{5} = \frac{2}{3} (2 x + 1)

Solve :

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

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(1) 2x − 5 = 1 (2) 3x − 2 = −7 (3) 4x + 7 = 15

(1) 2x − 5 = 1 ⇒ 2x = 6 ⇒ x = 6 ÷ 2 ∴ x = 3 (2) 3x − 2 = −7 ⇒ 3x = −5 ⇒ x = -53 ∴ x = -53 (3) 4x + 7 = 15 ⇒ 4x = 8 ⇒ x = 84 ∴ x = 2

(1) 2x − 5 = 1
(2) 3x − 2 = −7
(3) 4x + 7 = 15

(1) 2x − 5 = 1
⇒ 2x = 6
⇒ x = 6 ÷ 2
∴ x = 3

(2) 3x − 2 = −7
⇒ 3x = −5
⇒ x = $\frac{- 5}{3}$
∴ x = $\frac{- 5}{3}$

(3) 4x + 7 = 15
⇒ 4x = 8
⇒ x = $\frac{8}{4}$
∴ x = 2