Problem

For each equation, choose the statement that describes its solution. If applicable, give the solution.
4(w+1)+5=6(w1)+w

No solution
w=

All real numbers are solutions
2(v+2)+v=3(v1)+6

No solution
v=

All real numbers are solutions

Answer

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Answer

The solution for the second equation is No solution

Steps

Step 1 :Distribute the 4 and 6 to the terms inside the parentheses for the first equation: 4(w+1)+5=6(w1)+w4w+4+5=6w6+w

Step 2 :Combine like terms for the first equation: 4w+4+5=6w6+w4w+9=7w6

Step 3 :Isolate the variable w on one side for the first equation: 4w+9=7w69+6=7w4w15=3w

Step 4 :Solve for w in the first equation: 15=3ww=153w=5

Step 5 :The solution for the first equation is w=5

Step 6 :Distribute the 2 and 3 to the terms inside the parentheses for the second equation: 2(v+2)+v=3(v1)+62v+4+v=3v3+6

Step 7 :Combine like terms for the second equation: 2v+4+v=3v3+63v+4=3v+3

Step 8 :Attempt to isolate the variable v on one side for the second equation: 3v+4=3v+34=3

Step 9 :Since 4 does not equal 3, there is no solution for the second equation

Step 10 :The solution for the second equation is No solution

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