Question

Solve for $|2x+3|+x=10$, 'x' is a real number

• A. $-13or\frac{7}{3}$
• B. $-7or\frac{13}{3}$
• C. $13or\frac{7}{3}$
• D. $7or-\frac{13}{5}$

Answer 1

The correct option is A $-13or\frac{7}{3}$

Case 1 $|2x+3|=-(2x+3)$
So, $-2x-3+x=10$
$-x-3=10$
$x=-13$
If case 2 $|2x+3|=(2x+3)$
$2x+3+x=10$
$3x=7$
or $x=\frac{7}{3}$
Since the conditions for x is consistent in either case, we have the solution for x as $x=-13or\frac{7}{3}$