Question

does the equation 4(x - 2) = 4x - 6 have one solution, no solutions, or infinitely many solutions? first, lets try to isolate the variable, x. one of the x terms is inside the parentheses on the left. so, lets start by getting rid of the parentheses to make this equation easier to work with. one way to do this is to distribute the 4 to the x and to the 2. start by distributing the 4 to the x. how can you show 4 · x using an expression? 4(x - 2) = 4x - 6 \boxed{ -?} = 4x - 6

Explanation:

Step1: Distribute 4 to the parentheses

$4(x-2) = 4x - 8$

Step2: Compare both sides of equation

$4x - 8 = 4x - 6$

Step3: Subtract $4x$ from both sides

$4x - 8 - 4x = 4x - 6 - 4x$
$-8 = -6$

Answer:

The equation has no solutions. The missing value in the box is $4x$ (to show $4 \cdot x$ as part of the distribution step, leading to the conclusion that the contradictory statement $-8=-6$ means no solutions exist).