Question

Determine whether the equation is always, sometimes, or never true. 2/3 * x + 4 = 2x

Answer 1

2 / 3 x + 4

and

2 x

are two linear equations.

Two linear equations, if they do not have the same slope, have only one point of contact, i.e. their value is equal only at one point.

Slope of first equation is 2 / 3.

Slope of second equation is 2.

So their value is equal only at one point.

2 / 3 x + 4 = 2 x

Subtract 2 / 3 x to bith sides.

4 = 2 x - 2 / 3 x

4 = 6 x / 3 - 2 / 3 x

4 = 4 / 3 x

Divide both sides by 4.

1 = 1 / 3 x

Multiply both sides by 3.

3 = x

x = 3

Check result.

2 / 3 x + 4 = 2 x

for x = 3

( 2 / 3 ) • 3 + 4 = 2 • 3

6 / 3 + 4 = 6

2 + 4 = 6

6 = 6

The equation is true only for x = 3.