Questions: Solve the equation for the given variable. If your answer is a fraction, write it in reduced, fractional form. Do NOT convert the answer to a decimal. 4(2x+4)=2(5x+4) Answer: x=

$Solve the equation for the given variable. If your answer is a fraction, write it in reduced, fractional form. Do NOT convert the answer to a decimal. 4(2x+4)=2(5x+4) Answer: x=$

Transcript text: Solve the equation for the given variable. If your answer is a fraction, write it in reduced, fractional form. Do NOT convert the answer to a decimal. \[ 4(2 x+4)=2(5 x+4) \] Answer: $x=$ $\square$

Solution

Solution Steps

To solve the equation $4(2x + 4) = 2(5x + 4)$, we will first expand both sides of the equation. Then, we will collect like terms and isolate the variable $x$ on one side of the equation. Finally, we will solve for $x$ and simplify the solution if necessary.

Step 1: Expand Both Sides of the Equation

Start by expanding both sides of the equation: \[ 4(2x + 4) = 2(5x + 4) \] Expanding gives: \[ 8x + 16 = 10x + 8 \]

Step 2: Collect Like Terms

Rearrange the equation to collect like terms. Subtract $8x$ from both sides: \[ 16 = 2x + 8 \]

Step 3: Isolate the Variable

Subtract 8 from both sides to isolate the term with $x$: \[ 8 = 2x \]

Step 4: Solve for $x$

Divide both sides by 2 to solve for $x$: \[ x = 4 \]