52. Complete two column proof. Given: x/6+2=15
Prove: x=78
x/6+2=15 A:______
x/6=13 B:______
x=78 C:_______
To complete the two-column proof, we will use algebraic manipulation to solve for x. Here is one possible way to proceed:
A: x/6 + 2 = 15 Statement
B: x/6 = 15 - 2 Subtraction Property of Equality
C: x/6 = 13 Simplification
D: (6 * x)/6 = 13 * 6 Multiplication Property of Equality
E: x = 78 Simplification
Let's go step by step and explain each statement:
Statement A: This is the given equation.
Statement B: We subtract 2 from both sides of the equation to isolate the term x/6. This is the Subtraction Property of Equality, which states that subtracting the same value from both sides of an equation maintains equality.
Statement C: We simplify the equation by evaluating 15 - 2, which gives us 13.
Statement D: In order to eliminate the fraction x/6, we multiply both sides of the equation by 6. This is the Multiplication Property of Equality, which states that multiplying both sides of an equation by the same nonzero value maintains equality.
Statement E: Simplifying the equation, the 6s on the left side cancel out, leaving us with x = 78.
Thus, we have proved that if x/6 + 2 = 15, then x = 78.
A: Subtract 2 from both sides of the equation to isolate x/6.
x/6 + 2 - 2 = 15 - 2
x/6 = 13
B: Multiply both sides of the equation by 6 to eliminate the fraction.
6 * (x/6) = 13 * 6
x = 78
C: Therefore, we have proven that x = 78 based on the given equation.
A is your statement of the problem
B subtract two from both sides
C multiply both sides by 6