Complete the two-column proof. Given: x/6 +2=15 prove x = 78 a. __________ b. __________ x = 78 c. ___________
a. Subtract 2 from both sides: x/6 + 2 - 2 = 15 - 2
x/6 + 0 = 13
Simplify: x/6 = 13
b. Multiply both sides by 6: 6(x/6) = 6(13)
x = 78
c. This was proved in step b.
a. Subtract 2 from both sides of the equation.
x/6 +2 - 2 = 15 - 2
x/6 = 13
b. Multiply both sides of the equation by 6 to isolate x.
6 * (x/6) = 13 * 6
x = 78
c. The original equation is now solved, which proves that x = 78.
a. Start by isolating the variable x. Subtract 2 from both sides of the equation to cancel out the 2 on the left side:
x/6 + 2 - 2 = 15 - 2
This simplifies to:
x/6 = 13
b. To solve for x, multiply both sides of the equation by 6 to cancel out the denominator of 6 on the left side:
6 * (x/6) = 6 * 13
The 6 cancels out on the left side, leaving:
x = 78
c. Finally, the two-column proof can be completed as follows:
Statement | Reason
-------------------------------------------------------
1. x/6 + 2 = 15 | Given
2. x/6 = 15 - 2 | Subtract 2 from both sides
3. x/6 = 13 | Simplify
4. 6 * (x/6) = 6 * 13 | Multiply both sides by 6
5. 1 * x = 78 | Simplify
6. x = 78 | Simplify