Answer:
x=x+1 is correct, -6x=-5(x-1)-1x is correct, 7(x-5)=x+13 is correct, x=x is correct, x+4=x+4 is correct.
5(x+2)=25 should go in one solution.
2x+2=2(x+1) should go into infinite solutions.
2x+3=2x+5 should go into no solution.
9x+1=9x should go into no solution.
2x+8=16 should go into one solution.
3x+1=31 should go into one solution.
Explanation:
Explanation(s):
5(x+2)=25:
One value of x will equal 25, which is 3. You can solve this in two ways, calculations or graphing. I will show you both ways. You'll get 5x+10 from 5(x+2). Then you can subtract ten from both sides to isolate x, 5x=15. Then divide both sides by five to find what x equals, which is three. By graphing both the equations 5x+10 and y=25, you'll find that both of the lines intersect at (3,25), the x value of the coordinate is what x will equal, and there's only one intersection so there's only one solution.
2x+2=2(x+1):
The equation will be the exact same on both sides, which means all values of x will be a solution. If you were to graph both equations, they'd overlap perfectly, resulting in an infinite amount of intersections.
2x+3=2x+5:
The equation cannot be simplified any further, and 2x+5 is transformed two units above the equation 2x+3. If you were to graph both of these equations, they will never intersect for any value of x, which means no solutions.
9x+1=9x:
The equation cannot be simplified any further, and 9x+1 is transformed one unit above the equation 9x. If you were to graph both of these equations, they will never intersect for any value of x, which means no solutions.
2x+8=16:
Subtract eight from both sides, then divide both sides by two to get x=4. This means that there is only one solution for the equation. Alternatively, you could graph 2x+8 and y=16, and they will intersect at the point (4,16), which is only one solution.
3x+1=31:
Subtract one from both sides, divide by three to get x=10. There is only going to be one solution for the equation. Graph 3x+1 and y=31 to find that both the lines intersect at (10,31).