Question

Which solution would make the following equation 2(4x - 3) - 8 = 4 + 2x true?

A. 1

B. 3

C. 2

D. 4​

Answer 1

Solution

$\\\sf{→2(4x - 3) - 8 = 4 + 2x}$

$\sf{→8x - 6 - 8 = 4 + 2x}$

$\sf{→8x - 14 = 4 + 2x}$

$\sf{→8x-2x=4+14}$

$\sf{→6x=18}$

$\bf{~~~~~ x=\gray{3}}$

• Option B is Correct

$\\\\\sf{Verification}$

$\rightsquigarrow2(4×3 - 3) - 8 = 4 + 2×3$

$\rightsquigarrow 2(12 - 3) - 8 = 4 + 6$

$\rightsquigarrow 2×9 - 8 = 10$

$\rightsquigarrow 18-8=10$

$\rightsquigarrow 10=10_{\sf Verified}$

Answer 2

Solution!!

2(4x - 3) - 8 = 4 + 2x

Distribute 2 through the parentheses.

8x - 6 - 8 = 4 + 2x

Calculate the difference.

8x - 14 = 4 + 2x

Move the variable to the left-hand side and change its sign.

8x - 14 - 2x = 4

Move the constant to the right-hand side and change its sign.

8x - 2x = 4 + 14

Group the like terms and calculate the difference.

6x = 4 + 14

Calculate the sum.

6x = 18

Calculate for x.

x = 18 ÷ 6

x = 3

Hence, the value of x is 3 for which the equation is true. Let's verify it!

2(4x - 3) - 8 = 4 + 2x

Taking LHS,

= 2(4x - 3) - 8

= 2(4(3) - 3) - 8

= 2(12 - 3) - 8

= 2(9) - 8

= 18 - 8

= 10

Taking RHS,

= 4 + 2x

= 4 + 2(3)

= 4 + 6

= 10

LHS = RHS

Hence, verified.