What two equations have the same solution?: 5x/9 = 3, 2 (5x + 4) = 8x + 28, 6x - 10 = 50, x/2 + 4 = 5x - 10

Answer 1

To determine which two equations have the same solution, we'll solve each equation one by one.

1. Equation 1: $\frac{5x}{9}=3$

   Multiply both sides by 9: $$5x=27$$ Divide both sides by 5: $$x=\frac{27}{5}=5.4$$

2. Equation 2: $2(5x+4)=8x+28$

   Distribute the 2: $$10x+8=8x+28$$ Subtract $8x$ from both sides: $$2x+8=28$$ Subtract 8 from both sides: $$2x=20$$ Divide by 2: $$x=10$$

3. Equation 3: $6x-10=50$

   Add 10 to both sides: $$6x=60$$ Divide by 6: $$x=10$$

4. Equation 4: $\frac{x}{2}+4=5x-10$

   Multiply everything by 2 to eliminate the fraction: $$x+8=10x-20$$ Subtract $x$ from both sides: $$8=9x-20$$ Add 20 to both sides: $$28=9x$$ Divide by 9: $$x=\frac{28}{9}\approx 3.11$$

Now, let's summarize the solutions:

• From Equation 1: $x=\frac{27}{5}=5.4$
• From Equation 2: $x=10$
• From Equation 3: $x=10$
• From Equation 4: $x=\frac{28}{9}\approx 3.11$

The equations that have the same solution are Equation 2 and Equation 3, both yielding $x=10$.