Find the value of \( x \) so that the ratios are equivalent. \( \begin{array}{lll}\text { 12. } 4 \text { to } 12 \text { and } 10 \text { to } x & \text { 13. } 36: 4 \text { and } x: 9 & \text { 14. } 0.5 \text { to } 7 \text { and } 3 \text { to } x \\ \text { Steps: } & \text { Steps: } & \text { Steps: } \\ x= & x= & x=\end{array} \)

To find the value of \( x \) for each of the given ratios, we need to set up proportions that reflect the equivalence of the ratios. **For 12. \( 4 \) to \( 12 \) and \( 10 \) to \( x \)**: Set up the proportion: \[ \frac{4}{12} = \frac{10}{x} \] Cross-multiply: \[ 4x = 12 \times 10 \] \[ 4x = 120 \] Now, divide by 4: \[ x = 30 \] So, \( x = 30 \). --- **For 13. \( 36: 4 \) and \( x: 9 \)**: Set up the proportion: \[ \frac{36}{4} = \frac{x}{9} \] Cross-multiply: \[ 36 \times 9 = 4x \] Calculating \( 36 \times 9 \): \[ 324 = 4x \] Now, divide by 4: \[ x = 81 \] So, \( x = 81 \). --- **For 14. \( 0.5 \) to \( 7 \) and \( 3 \) to \( x \)**: Set up the proportion: \[ \frac{0.5}{7} = \frac{3}{x} \] Cross-multiply: \[ 0.5x = 7 \times 3 \] Calculating \( 7 \times 3 \): \[ 0.5x = 21 \] Now, divide by 0.5 (or multiply by 2): \[ x = 42 \] So, \( x = 42 \). In summary, the values of \( x \) are: - \( x = 30 \) for the first ratio, - \( x = 81 \) for the second ratio, - \( x = 42 \) for the third ratio.