To solve for [tex]\( x \)[/tex] in the ratio equation [tex]\( 2:26 = 4:x \)[/tex]:
1. Understand the Ratio:
- The given ratio [tex]\( 2:26 \)[/tex] can be written as the fraction [tex]\(\frac{2}{26}\)[/tex].
- Similarly, the unknown ratio [tex]\( 4:x \)[/tex] can be written as [tex]\(\frac{4}{x}\)[/tex].
2. Set Up the Equation:
- Since the ratios are equivalent, we can write the equation:
[tex]\[
\frac{2}{26} = \frac{4}{x}
\][/tex]
3. Cross-Multiply:
- To solve for [tex]\( x \)[/tex], we cross-multiply:
[tex]\[
2 \cdot x = 26 \cdot 4
\][/tex]
4. Simplify the Right Side:
- First, calculate [tex]\( 26 \cdot 4 \)[/tex]:
[tex]\[
26 \cdot 4 = 104
\][/tex]
5. Set Up the Simplified Equation:
- Substituting back, we get:
[tex]\[
2x = 104
\][/tex]
6. Solve for [tex]\( x \)[/tex]:
- To isolate [tex]\( x \)[/tex], divide both sides of the equation by 2:
[tex]\[
x = \frac{104}{2} = 52
\][/tex]
Thus, the value of [tex]\( x \)[/tex] is [tex]\( 52 \)[/tex]. The detailed solution steps confirm that [tex]\( x = 52 \)[/tex].
