Problem 122 - Introductory Algebra for College Students

Question

Determine whether the given number is a solution of the equation. $$12-3(x-2)=4 x-(x+3) ; 3 \frac{1}{2}$$

Step-by-Step Solution

Answer

No, \(3 \frac{1}{2}\) is not a solution to the initial equation because 7/2 is not equal to 21/6.

Step 1: Simplify the equation

Distribute the -3 on the left side of the equation across \(x-2\) : \(12 - 3x + 6 = 4x - x - 3\). Combine like terms to have \(18 - 3x = 3x - 3\).

Step 2: Reorder the simplified equation

Get all x terms on one side and numbers on the other side of the equation: \(6x = 21\). Therefore, after simplification, the initial equation is equivalent to \(x = 21 / 6\)

Step 3: Substitute the value for x in the equation

Substitute the given number \(3 \frac{1}{2}\) (which is 7/2 in fraction form) for 'x' in the equation \(x = 21 / 6\) (which is 3.5 in decimal form). Check if both sides of the equation are equal.