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Which equation has no solution? 5+2(3+2x)=x+3(x+1) 5(x+3)+x=4(x+3)+3 4(x+3)+2x=6(x+2) 4+6(2+x)=2(3x+8)

Which equation has no solution?\newline5+2(3+2x)=x+3(x+1) 5+2(3+2 x)=x+3(x+1) \newline5(x+3)+x=4(x+3)+3 5(x+3)+x=4(x+3)+3 \newline4(x+3)+2x=6(x+2) 4(x+3)+2 x=6(x+2) \newline4+6(2+x)=2(3x+8) 4+6(2+x)=2(3 x+8)

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Full solution

Q. Which equation has no solution?\newline5+2(3+2x)=x+3(x+1) 5+2(3+2 x)=x+3(x+1) \newline5(x+3)+x=4(x+3)+3 5(x+3)+x=4(x+3)+3 \newline4(x+3)+2x=6(x+2) 4(x+3)+2 x=6(x+2) \newline4+6(2+x)=2(3x+8) 4+6(2+x)=2(3 x+8)
  1. Simplify the first equation: First, let's simplify the first equation: 5+2(3+2x)=x+3(x+1)5 + 2(3 + 2x) = x + 3(x + 1). Distribute the 22 into (3+2x)(3 + 2x): 5+6+4x=x+3x+35 + 6 + 4x = x + 3x + 3. Combine like terms: 11+4x=4x+311 + 4x = 4x + 3. Subtract 4x4x from both sides: 11=311 = 3. Since 1111 does not equal 33, this equation has no solution.

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