sort each equation according to whether it has one solution, infinitely many solutions, or no solution.\n5(x…

sort each equation according to whether it has one solution, infinitely many solutions, or no solution.\n5(x - 2)=5x - 7\n-3(x - 4)=-3x + 12\n4(x + 1)=3x + 4\n-2(x - 3)=2x - 6\n6(x + 5)=6x + 11\none solution\ninfinitely many solutions\nno solution

sort each equation according to whether it has one solution, infinitely many solutions, or no solution.\n5(x - 2)=5x - 7\n-3(x - 4)=-3x + 12\n4(x + 1)=3x + 4\n-2(x - 3)=2x - 6\n6(x + 5)=6x + 11\none solution\ninfinitely many solutions\nno solution

Answer

Answer:

  • One Solution: $4(x + 1)=3x + 4$, $-2(x - 3)=2x - 6$
  • Infinitely Many Solutions: $-3(x - 4)=-3x + 12$
  • No Solution: $5(x - 2)=5x - 7$, $6(x + 5)=6x + 11$

Explanation:

Step1: Simplify $5(x - 2)=5x - 7$

Expand left - hand side: $5x-10 = 5x - 7$. Subtract $5x$ from both sides, we get $-10=-7$, which is false, so no solution.

Step2: Simplify $-3(x - 4)=-3x + 12$

Expand left - hand side: $-3x + 12=-3x + 12$. This is an identity, so infinitely many solutions.

Step3: Simplify $4(x + 1)=3x + 4$

Expand left - hand side: $4x+4 = 3x + 4$. Subtract $3x$ from both sides and then subtract 4 from both sides, we get $x = 0$, one solution.

Step4: Simplify $-2(x - 3)=2x - 6$

Expand left - hand side: $-2x + 6=2x - 6$. Add $2x$ to both sides and then add 6 to both sides, $12 = 4x$, $x = 3$, one solution.

Step5: Simplify $6(x + 5)=6x + 11$

Expand left - hand side: $6x+30 = 6x + 11$. Subtract $6x$ from both sides, we get $30 = 11$, which is false, so no solution.