Algebraic Equations and Expressions

2x - 12 = -4x - 24 Bring subject terms to one side and non subject terms to another side 2x + 4x = -24 + 12 6x = -12 Dividing both sides by 6 x = -2

–48x + 36 = -18x – 174    Bring subject terms on one side and non subject terms on another side 48x – 18x = 174 + 36 30x = 210 Dividing both sides by 30 x = 7

8x + 10 = 10x Subtract 8x from both side 10x - 8x = 10 2x = 10 Dividing both sides by 2, we get x = 5

Assume X as 3. Then (1) = 8, (2) = 21, (3) = 33, (4) = 29 and (5) = 14. So (1) and (5) is not the answer. Let take X = 2 then (2) = 11, (3) = 18, and (4) = 14. Only choice (2) is odd in both cases.

Left side: (12x)_3 = 1 * 3^2 + 2 * 3^1 + x * 3^0 = 9 + 6 + x = 15 + x. Right side: (123)_x = 1 * x^2 + 2 * x^1 + 3 * x^0 = x^2 + 2x + 3. Solving: 15 + x = x^2 + 2x + 3, so x^2 + x - 12 = 0, giving x = 3 or x = -4. Since base must be > 3 (digit 3 present), x = 3.

2x + 3 = 4 Or 2x = 1 Or 4x = 2 Therefore, 4x + 2 = 4

The given equation is 3(2x + 1) = 7. According to the distributive property of multiplication, 3 × 2x + 3 × 1 = 76x + 3 = 7 Transposing 3 to R.H.S, we get: 6x = 7 – 36x = 4 Dividing both sides of the equation by 6, we get: x = 4/6 = 2/3 The required value of x is 2/3. Thus, the required value of (4x – 3) is -1/3. This answer is correct.

The given equation is 2(3x - 4) = 6 According to the distributive property of multiplication,  3 x -4 = 3 3x  =  3 + 4   x = 7/3

Now, (5x + 2) = 5(7/3) + 2 = 35/3  + 2 = 41/3 This answer is correct.

Yes, - 3/2 + 1/2 = - 1 is the correct answer.

9/x = 3 9/3 = x 3 = x x = 3

8x - 8 = 56 8x = 56 + 8 8x = 64 x = 64/8 x = 8

(x + 1/x) = 3    (x + 1/x)² = 9     Or  x² + 1/x² + 2 = 9          x² + 1/x² = 7

( X = 2, SO X + 4 WILL BECOME 2 + 4 = 6)

x² + 5x + k = 5 x = 0 0² + 5(0) + k = 5 k = 5

since x is under square root, so squaring both sides we get18*14*x=84*84x= (84 * 84) / (18 * 14)therefore, x=28hence, Correct answer