translating statements; solving linear equations

[SherryG]

1) Translate to an algebra statement. Do not solve:

"Five times the difference of a number and one yields the same result as twice the same number increased by three."

2) Solve for x: 1 + 3x = -2x - 9

3) Solve for x: 8(x - 1) + 3 = 7x - 6 - 5x

4) Solve for x: (x - 5)/3 - 3/2 = (4x + 7)/6

If you can explain the process that you did to receive the answer, that will help me as a guide to the many problems that I am experiencing.

Thank you all again.

 

[stapel]

1) i) Pick a variable for "a number".

ii) Write an expression, in terms of the variable in (i), for "the difference of a number and 1".

iii) Write an expression, in terms of (ii), for "five times" this difference.

iv) Write an expression, in terms of (i), for "twice the number".

v) Write an expression, in terms ov (iv), for twice the number "increased by 3".

vi) Write an equation, in terms of (iii) and (v), for "yields the same result" (that is, "is equal to").

2) Add 2x to both sides. Subtract 1 from both sides. Divide through by 5.

3) Multiply the 8 through the x - 1. Simplify on both sides. Then follow steps similar to those in (2).

4) Multiply through by 6 to clear the denominators. Then proceed similarly to (2) and (3).

If you get stuck, please reply showing your work. Thank you.

Eliz.