Chapter 5.5, Problem 41E

(a)

To determine

the sign of the solution for the equation $ax+b=cx+d$

Answer to Problem 41E

The solution (x-value) is NEGATIVE

Explanation of Solution

Given information:

The given equation is $ax+b=cx+d$ in $0<b<d;a<c$

Formula used:

Graph method is used.

Calculation:

0 < b < d implies that the y-intercept is at the y-axis.

a < c implies that the point of intersection occurs somewhere to the left of the -axis.

Therefore, the solution (x-value) is NEGATIVE

Conclusion:

The solution (x-value) is NEGATIVE

(b)

To determine

the sign of the solution for the equation $ax+b=cx+d$

Answer to Problem 41E

The solution (x-value) is POSITIVE.

Explanation of Solution

Given information:

The given equation is $ax+b=cx+d$ in $d<b<0;a<c$

Formula used:

Graph method is used.

Calculation:

d < b < 0 implies that the y-intercept is at the -y-axis.

a < c implies that the point of intersection occurs somewhere to the right of the -axis.

Therefore, the solution (x-value) is POSITIVE.

Conclusion:

The solution (x-value) is POSITIVE.