# Math Help - solving the equation

1. ## solving the equation

Solve:

2x + 3 = |4x - 7|

2. Originally Posted by Mr_Green
Solve:

2x + 3 = |4x - 7|

There are two cases to consider:

1. 4x-7>=0

then we need to solve:

2x+3 = 4x-7

which has solution: x=5, which we need to check satisfies the assumed
condition 4x-7 >=0, which it does so x=5 is a solution.

2. 4x-7<0

then we need to solve:

2x+3 = -(4x-7)

or:

6x = 4,

so x=2/3. Now check this in the assumed condition 4x-7<0, which it passes
so x=2/3 is also a solution.

Hence the solutions are x=5, and x=2/3.

RonL

3. Originally Posted by Mr_Green
Solve:

2x + 3 = |4x - 7|

$\sqrt{x^2}=|x|$
$2x+3=\sqrt{(4x-7)^2}$
$(2x+3)^2=(4x-7)^2$