Given: 4(5 + 7) − 3 = 3(4 − 9)
Prove: = −11
Statement:
1.) 4(5 + 7) − 3 = 3(4 − 9) ====> Given
2.) 20 + 28 − 3 = 12 − 27 ====> Distributive property of multiplication
3.) Madison has ====> 17n + 28 When she should have ====> used 17 − 39 = 12 − 27 Madison Simply instead she should have used ======> Subtraction
4.) 5 + 28 = −27 she uses the Subtraction Property of Equality ======> She Should use ====> Subtraction property of equality
5.) 5n = −55 Madison used the Multiplication Property of Equality ====> Instead of using the =====> Subtraction property of equality
6.) n = −11 =======> Division property of equality
Showing Work:
Simplifying
4(5n + 7) + -3n = 3(4n + -9)
Reorder the terms:
4(7 + 5n) + -3n = 3(4n + -9)
(7 * 4 + 5n * 4) + -3n = 3(4n + -9)
(28 + 20n) + -3n = 3(4n + -9)
Combine like terms:
20n + -3n = 17n
28 + 17n = 3(4n + -9)
Reorder the terms:
28 + 17n = 3(-9 + 4n)
28 + 17n = (-9 * 3 + 4n * 3)
28 + 17n = (-27 + 12n)
Solving
28 + 17n = -27 + 12n
Solving for variable 'n'.
Move all terms containing n to the left, all other terms to the right.
Add '-12n' to each side of the equation.
28 + 17n + -12n = -27 + 12n + -12n
Combine like terms:
17n + -12n = 5n
28 + 5n = -27 + 12n + -12n
Combine like terms:
12n + -12n = 0
28 + 5n = -27 + 0
28 + 5n = -27
Add '-28' to each side of the equation.
28 + -28 + 5n = -27 + -28
Combine like terms:
28 + -28 = 0
0 + 5n = -27 + -28
5n = -27 + -28
Combine like terms:
-27 + -28 = -55
5n = -55
Divide each side by '5'.
n = -11
Simplifying
n = -11
Hope that helps!!!! :)