Solve for x using
cross multiplication.
2x + 1
3
x + 2
2
x= [?]
Enter

Step 1

Make the right side of the equation a fraction:

3

x

2

+

2

x

−

1

x

2

−

1

=

−

2

1

Step 2

Cross multiply:

−

1

(

3

x

2

+

2

x

−

1

)

=

−

2

(

x

2

−

1

)

−

3

x

2

−

2

x

+

1

=

−

2

x

2

+

2

Step 3

Simplify:

−

2

x

+

1

=

−

2

x

2

+

3

x

2

+

2

−

2

x

+

1

=

x

2

+

2

−

2

x

=

x

2

+

1

0

=

x

2

+

2

x

+

1

Step 4

Solve for

x

:

0

=

x

2

+

2

x

+

1

We notice that the above represents the expanded form of the perfect square:

0

=

(

x

+

1

)

2

Because of the perfect square, we know that x has only one value:

x

=

−

1

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

step-by-step explanation:

points a and b are equidistant from the desired line, so the line you find by using them will go through point r.

using points other than a and b will give the desired line only if they are equidistant from r. if they are randomly located, the perpendicular line you create will not necessarily go through point r, hence will not be a solution to the problem.