reasoning about numbers

Question

1. Explain how to solve the 2 equations below by reasoning about numbers,
2. operations, and expressions INSTEAD OF using standard algebraic equation- solving techniques.
3. 𝑪+𝟑𝟒×𝟖=𝟐𝟖×𝟑𝟒
4. 𝟏𝟖𝟕(𝒙 − 𝟒𝟏𝟗)𝟐 = 𝟎
5. 𝑪𝟕.𝟗𝒙+𝟑.𝟐=𝟕𝟗𝟑.𝟐

Answer 1

a C+34x8 = 28x34

C = 28x34 -8x34

C = (28-8) x 34

C = 20x34

C = 680

680+272 = 952

b 187(x-419)2 =0

x=419

187(419-419)2 =0

187(0)2 =0

(0)2 = 0

0 = 0

x= 419 regardless whether you intended to write 187(x-419)^2 = 0 or 187(x-419)(2) = 0

c C7.9x + 3.2 = 793.2

C7.9x = 793.2 -3.2

C7.9x = 7900 + 3.2 - 3.2

C7.9x = 7900

Cx = 7900/7.9

Cx = 1000

x = 1000/C

or C = 1000/x