Question

algebra i with probability young ic on a continuous learning center - credit bearing (tutor) solving linear equations: distributive property sorting solutions of equations sort each equation according to whether it has one solution, infinitely many solutions, or no solution. -2(x - 3)=2x - 6 -3(x - 4)=-3x + 12 5(x - 2)=5x - 7 6(x + 5)=6x + 11 4(x + 1)=3x + 4 one solution infinitely many solutions no solution

Explanation:

Step1: Simplify the first equation -2(x - 3)=2x - 6

Expand the left - hand side using the distributive property: -2x+6 = 2x - 6.
Add 2x to both sides: 6 = 4x - 6.
Add 6 to both sides: 12 = 4x.
Divide both sides by 4: x = 3. So it has one solution.

Step2: Simplify the second equation -3(x - 4)=-3x + 12

Expand the left - hand side: -3x+12=-3x + 12.
Subtract (-3x + 12) from both sides: 0 = 0. This equation is an identity and has infinitely many solutions.

Step3: Simplify the third equation 5(x - 2)=5x - 7

Expand the left - hand side: 5x-10 = 5x - 7.
Subtract 5x from both sides: -10=-7, which is a false statement. So it has no solution.

Step4: Simplify the fourth equation 6(x + 5)=6x + 11

Expand the left - hand side: 6x+30 = 6x + 11.
Subtract 6x from both sides: 30 = 11, which is a false statement. So it has no solution.

Step5: Simplify the fifth equation 4(x + 1)=3x + 4

Expand the left - hand side: 4x+4 = 3x + 4.
Subtract 3x from both sides: x+4 = 4.
Subtract 4 from both sides: x = 0. So it has one solution.

Answer:

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