# Solve.Be careful to examine work to see if the equation has no solution or an infinite number of solutions A) -1+5(x-2)=12x+3-7x B)9(x+3)-6=24-2x-3+11x

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(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.**

A. -1+5x-10=12x+3-7x

-11+5x=5x+3

There is no solution offered.

B. 9x+27-6=24-2x-3+11x

9x+21 = 21+9x

infinite number of solution since LHS = RHS