82+ 5 = 14x 2) 47= 2r-3 3) 12+2r= +2r=0 4) 672 - 12= 0 5) 3r + 45 - 24x=0 6) 4r + 4r + 1 = 0 7) 3y7 + 7y-6= 0

Let's solve each equation step-by-step: 1) **Equation:** \( 82 + 5 = 14x \) **Solution:** \( 87 = 14x \) \( x = \frac{87}{14} \) \( x \approx 6.2143 \) 2) **Equation:** \( 47 = 2r - 3 \) **Solution:** \( 50 = 2r \) \( r = \frac{50}{2} = 25 \) 3) **Equation:** \( 12 + 2r + 2r = 0 \) **Solution:** Combine like terms: \( 12 + 4r = 0 \) \( 4r = -12 \) \( r = \frac{-12}{4} = -3 \) 4) **Equation:** \( 672 - 12 = 0 \) **Solution:** \( 660 = 0 \) This is not a valid equation (it states that 660 equals 0, which is false). 5) **Equation:** \( 3r + 45 - 24x = 0 \) **Solution:** Rearranging gives: \( 3r = 24x - 45 \) This can be expressed as \( r = \frac{24x - 45}{3} \). Simplifying further: \( r = 8x - 15 \) 6) **Equation:** \( 4r + 4r + 1 = 0 \) **Solution:** Combine like terms: \( 8r + 1 = 0 \) \( 8r = -1 \) \( r = \frac{-1}{8} = -0.125 \) 7) **Equation:** \( 3y^7 + 7y - 6 = 0 \) This is a polynomial equation and usually requires numerical methods or graphical solutions for specific values of \( y \). It cannot be solved algebraically for exact roots without additional context. Please let me know if you have any further questions or if you'd like to explore any of these solutions in more detail!