To solve the equation
[tex]\[ \frac{5-2x}{4} = 2x, \][/tex]
follow these steps:
1. Eliminate the fraction: Multiply both sides of the equation by 4 to get rid of the denominator.
[tex]\[4 \cdot \frac{5-2x}{4} = 4 \cdot 2x\][/tex]
This simplifies to:
[tex]\[5 - 2x = 8x\][/tex]
2. Isolate the variable term: To isolate the term involving [tex]\(x\)[/tex], add [tex]\(2x\)[/tex] to both sides of the equation.
[tex]\[5 - 2x + 2x = 8x + 2x\][/tex]
Simplifying the equation gives:
[tex]\[5 = 10x\][/tex]
3. Solve for [tex]\(x\)[/tex]: Now, isolate [tex]\(x\)[/tex] by dividing both sides of the equation by 10.
[tex]\[x = \frac{5}{10}\][/tex]
Simplifying the fraction gives:
[tex]\[x = \frac{1}{2}\][/tex]
So, the solution to the equation [tex]\(\frac{5-2x}{4} = 2x\)[/tex] is
[tex]\[ x = \frac{1}{2}. \][/tex]
This means that [tex]\( x = \frac{1}{2} \)[/tex] satisfies the given equation.
