Select all of the equations below that are equivalent to:−21=f−gUse properties of equality.Multi-select Choices:(A) 5=−3f−g(B) −7=3f−g(C) 3=−7f−g(D) −4=7f−g
Q. Select all of the equations below that are equivalent to:−21=f−gUse properties of equality.Multi-select Choices:(A) 5=−3f−g(B) −7=3f−g(C) 3=−7f−g(D) −4=7f−g
Identify Equation & Task: Identify the original equation and understand the task.The original equation is −21=f−g. We need to find which of the given choices are equivalent to this equation by using properties of equality.
Analyze Choice (A): Analyze choice (A) 5=f−−3g. To check if this equation is equivalent to −21=f−g, we need to multiply both sides of the equation by −3. 5×(−3)=(f−−3g)×(−3)−15=f−g This equation is not equivalent to −21=f−g.
Analyze Choice (B): Analyze choice (B) −7=f−3g. To check if this equation is equivalent to −21=f−g, we need to multiply both sides of the equation by 3. (−7)×3=(f−3g)×3−21=f−g This equation is equivalent to −21=f−g.
Analyze Choice (C): Analyze choice (C) 3=f−−7g. To check if this equation is equivalent to −21=f−g, we need to multiply both sides of the equation by −7. 3×(−7)=(f−−7g)×(−7)−21=f−g This equation is equivalent to −21=f−g.
Analyze Choice (D): Analyze choice (D) −4=f−7g. To check if this equation is equivalent to −21=f−g, we need to multiply both sides of the equation by 7. (−4)×7=(f−7g)×7−28=f−g This equation is not equivalent to −21=f−g.