   Chapter 0.5, Problem 12E

Chapter
Section
Textbook Problem

Solve the equations in Exercises 1–12 for x (mentally, if possible). x − 1 = c x + d         ( c ≠ 1 )

To determine

To calculate: The value of x in the linear equation x1=cx+d (c1).

Explanation

Given Information:

The provided linear equation is x1=cx+d (c1).

Formula used:

Linear equation ax+b=0 where a and b are fixed numbers with a0.

Step:1 Subtract b from both sides in the given equation.

Step:2 Divide by a on both sides in the given equation.

Calculation:

Consider the linear equation x1=cx+d (c1).

Add dcx on both sides from the above equation then simplify,

x1dcx=cx+ddcx

Make the group then take out common value in the above equation,

x1dcx=cx+ddcxxcx1d=0x(1c)1d=0

Add 1+d on both sides in the above equation,

x1dcx=cx+ddcxxcx1d=0x(1c)1d=0x(1c)1d+1+d=0+1+d

Further solve the above expression

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