GuideFoot - Learn Together, Grow Smarter. Logo

In Mathematics / College | 2025-07-03

Solve the expression for $x$: $(4-2)(x-2)=4x-8$
A. $x=0$
B. $x=6 / 5$
C. $x=2$
D. $x=-2

Asked by jvergiels0001

Answer (2)

Simplify the left side of the equation: ( 4 − 2 ) ( x − 2 ) = 2 x − 4 .
Rewrite the equation: 2 x − 4 = 4 x − 8 .
Isolate x : 2 x = 4 .
Solve for x : x = 2 . The final answer is 2 ​ .

Explanation

Understanding the Problem We are given the equation ( 4 − 2 ) ( x − 2 ) = 4 x − 8 and asked to solve for x . Let's break down the steps to find the value of x that satisfies this equation.

Simplifying the Left Side First, simplify the left side of the equation: ( 4 − 2 ) ( x − 2 ) = 2 ( x − 2 ) = 2 x − 4 .

Rewriting the Equation Now, rewrite the equation with the simplified left side: 2 x − 4 = 4 x − 8 .

Isolating x Terms Next, subtract 2 x from both sides of the equation to isolate the x terms on one side: 2 x − 4 − 2 x = 4 x − 8 − 2 x , which simplifies to − 4 = 2 x − 8 .

Isolating Constant Terms Now, add 8 to both sides of the equation to isolate the constant terms on the other side: − 4 + 8 = 2 x − 8 + 8 , which simplifies to 4 = 2 x .

Solving for x Finally, divide both sides by 2 to solve for x :
2 4 ​ = 2 2 x ​ , which simplifies to x = 2 .

Verifying the Solution To verify the solution, substitute x = 2 into the original equation: ( 4 − 2 ) ( 2 − 2 ) = 2 ( 0 ) = 0 and 4 ( 2 ) − 8 = 8 − 8 = 0 . Since both sides are equal, the solution is correct.

Final Answer Therefore, the solution to the equation ( 4 − 2 ) ( x − 2 ) = 4 x − 8 is x = 2 .


Examples
In real-world scenarios, solving linear equations like this can help determine the break-even point in business. For example, if a company's cost is represented by 4 x − 8 and their revenue is ( 4 − 2 ) ( x − 2 ) , finding the value of x where cost equals revenue helps determine the number of units needed to be sold to break even. This type of problem also appears in physics, where you might need to solve for a variable in a linear motion equation.

Answered by GinnyAnswer | 2025-07-03

The value of x that satisfies the equation ( 4 − 2 ) ( x − 2 ) = 4 x − 8 is x = 2 . This was found after simplifying and solving the equation. The correct multiple choice answer is C . x = 2 .
;

Answered by Anonymous | 2025-07-04

Related Questions in Mathematics

📝 Answered - Select the correct answer. Which equation is equivalent to the given equation? [tex]$x^2-6 x=8$[/tex] A. [tex]$(x-6)^2=44$[/tex] B. [tex]$(x-3)^2=17$[/tex] C. [tex]$(x-6)^2=20$[/tex] D. [tex]$(x-3)^2=14$[/tex]

📝 Answered - Which phrase best describes the translation from the graph [tex]y=6 x^2[/tex] to the graph of [tex]y=6(x+1)^2[/tex]? A. 6 units left B. 6 units right C. 1 unit left D. 1 unit right

📝 Answered - What expression is equivalent to [tex]$\left(5 z^2+3 z+2\right)^2$[/tex] ? A. [tex]$5 z^4+3 z^2+4$[/tex] B. [tex]$5 z^4+9 z^2+4$[/tex] C. [tex]$25 z^4+30 z^3+19 z^2+12 z+4$[/tex] D. [tex]$25 z^4+30 z^3+29 z^2+12 z+4$[/tex]

📝 Answered - The graph of [tex]y=\frac{5}{4} x+1[/tex] is shown below. The coordinate ([tex]0, y[/tex]) is a solution of the equation. Given the [tex]x[/tex]-value of 0, what is the value of the [tex]y[/tex]-coordinate for the coordinate ([tex]0, y[/tex])? [tex]y=[/tex] [blank]

📝 Answered - If [tex]f(-2)=0[/tex], what are all the factors of the function [tex]f(x)=x^3-2 x^2-68 x-120[/tex]? Use the Remainder Theorem. A. [tex](x+2)(x+60)[/tex] B. [tex](x-2)(x-60)[/tex] C. [tex](x-10)(x+2)(x+6)[/tex] D. [tex](x+10)(x-2)(x-6)[/tex]