Question

Consider the equation 5 – 3(2x – 7) = 12 – 5(x – 2). Is x = 2 a solution to this

equation? Is x = 4 a solution to this equation?

Answer 1

Answer: No (x = 2), Yes (x = 4)

Explanation:

=> 5 - 3(2x - 7) = 12 - 5(x - 2)

Substitute x = 2 in the Equation :-

5 - 3(2x - 7) = 12 - 5(x - 2)
5 - 3(2(2) - 7) = 12 - 5((2) - 2)
5 - 3(4 - 7) = 12 - 5(2 - 2)
5 - 3(-3) = 12 - 5
5 + 9 = 12 - 5
14 = 7
LHS is not Equal to RHS

Therefore, x = 2 is not a Solution.

Substitute x = 4 in the Equation :-

5 - 3(2x - 7) = 12 - 5(x - 2)
5 - 3(2(4) - 7) = 12 - 5((4) - 2)
5 - 3(8 - 7) = 12 - 5(4 - 2)
5 - 3(1) = 12 - 5(2)
5 - 3 = 12 - 10
2 = 2
LHS is Equal to RHS

Therefore, x = 4 is a Solution.

Answer 2

`\sf x=4`

Explanation:

`\sf 5 - 3(2x - 7)=12 - 5(x - 2)`

To get rid of the parentheses, we'll apply the distributive property. Staring with the left side, multiply -3 by (2x-7).

`\sf 5 - 6x+21=12 - 5(x - 2)`

5+ 21= 26

`\sf 26 - 6x=12 - 5(x - 2)`

Now, let's do the same thing to the right side. Multiply -5 by (x-2) »12−5x+10, than add 12+ 10 = 22 .

`\sf 26 - 6x=22 - 5x`

Combine like terms.

`\sf 26 - x=22`

Subtract 26 from both sides.

`\sf - x= - 4`

Multiply both sides by -1.

`\sf x=4`