Which of these equations has no solutions?Choices:(A) 31(9x+3)=4x+5+x(B) −3(x+5)=−x−2x−15(C) −2x+5+8x=3(2x−1)Which statement explains a way you can tell the equation has no solutions?Choices:(A) It is equivalent to an equation that has the same variable terms but different constant terms on either side of the equal sign.(B) It is equivalent to an equation that has the same variable terms and the same constant terms on either side of the equal sign.(C) It is equivalent to an equation that has different variable terms on either side of the equation.
Q. Which of these equations has no solutions?Choices:(A) 31(9x+3)=4x+5+x(B) −3(x+5)=−x−2x−15(C) −2x+5+8x=3(2x−1)Which statement explains a way you can tell the equation has no solutions?Choices:(A) It is equivalent to an equation that has the same variable terms but different constant terms on either side of the equal sign.(B) It is equivalent to an equation that has the same variable terms and the same constant terms on either side of the equal sign.(C) It is equivalent to an equation that has different variable terms on either side of the equation.
Simplify equation (A): Simplify equation (A) 31(9x+3)=4x+5+x. Distribute and combine like terms:31×9x+31×3=4x+5+x3x+1=5x+5
Solve for x: Solve for x in equation (A): 3x+1=5x+51−5=5x−3x−4=2xx=−2
Simplify equation (B): Simplify equation (B) −3(x+5)=−x−2x−15. Distribute and combine like terms:−3x−15=−3x−15
Infinitely many solutions: Since equation (B) simplifies to −3x−15=−3x−15, which is always true, it has infinitely many solutions.
Simplify equation (C): Simplify equation (C) −2x+5+8x=3(2x−1). Distribute and combine like terms: 6x+5=6x−3
Solve for x: Solve for x in equation (C): 6x+5=6x−35=−3