(a) Solve -1+5(x-2)=12x+3-7x
Use the distributive property to clear the parantheses:
-1+5x-10=12x+3-7x Add(collect) like terms on both sides
5x-11=5x+3 Subtract 5x from both sides
-11=3 which is not true for any value of x.
There is no solution to the equation.
(b) Solve 9(x+3)-6=24-2x-3+11x Again use the dist. prop.
9x+27-6=24-2x-3+11x Add like terms
9x+21=9x+21 Subtract 9x from both sides
21=21 This is true for all values of x.
There is no solution offered.
9x+21 = 21+9x
infinite number of solution since LHS = RHS