Enter the value for X that makes the equation 1/2 (4x-8) + 3x = 36 true
The Correct Answer and Explanation is:
To solve the equation:12(4x−8)+3x=36\frac{1}{2}(4x – 8) + 3x = 3621(4x−8)+3x=36
Step 1: Distribute the 12\frac{1}{2}21
Apply the distributive property to the expression inside the parentheses:12⋅4x=2xand12⋅(−8)=−4\frac{1}{2} \cdot 4x = 2x \quad \text{and} \quad \frac{1}{2} \cdot (-8) = -421⋅4x=2xand21⋅(−8)=−4
So the equation becomes:2x−4+3x=362x – 4 + 3x = 362x−4+3x=36
Step 2: Combine like terms
Now combine the terms with xxx:(2x+3x)−4=36⇒5x−4=36(2x + 3x) – 4 = 36 \Rightarrow 5x – 4 = 36(2x+3x)−4=36⇒5x−4=36
Step 3: Solve for xxx
Add 4 to both sides:5x−4+4=36+4⇒5x=405x – 4 + 4 = 36 + 4 \Rightarrow 5x = 405x−4+4=36+4⇒5x=40
Now divide both sides by 5:x=405=8x = \frac{40}{5} = 8x=540=8
Final Answer:
8\boxed{8}8
Explanation
This problem involves solving a linear equation with one variable. The original equation contains a fraction and parentheses, indicating that the distributive property must be applied. The goal is to isolate the variable xxx and determine its value.
The first step is to simplify the expression 12(4x−8)\frac{1}{2}(4x – 8)21(4x−8) by distributing the 12\frac{1}{2}21 across both terms inside the parentheses. Multiplying 12\frac{1}{2}21 by 4x4x4x results in 2x2x2x, and multiplying 12\frac{1}{2}21 by −8-8−8 gives −4-4−4. The expression now reads:2x−4+3x=362x – 4 + 3x = 362x−4+3x=36
Next, like terms are combined. The terms 2x2x2x and 3x3x3x are both coefficients of xxx, and they add up to 5x5x5x. The equation is now simplified to:5x−4=365x – 4 = 365x−4=36
The next step is to isolate the variable term. This involves eliminating the constant term on the left-hand side by adding 4 to both sides of the equation, yielding:5x=405x = 405x=40
Finally, divide both sides of the equation by 5 to solve for xxx, resulting in:x=8x = 8x=8
This value of xxx satisfies the original equation, as substituting it back in would yield a true statement. This step-by-step method emphasizes the importance of applying algebraic operations consistently and logically to arrive at a correct solution.
