Question

3|х+2|+2|х+2|=5; help

Answer 1

Ответ:

3|x+2|+2|x+2|=5

5|x+2|=5

|x+2|=1

x+2=1 x=1-2 x=-1

x+2=-1 x=-1-2 x=-3

Answer 2

To solve the equation $3|х+2|+2|х+2|=5$, you can follow these steps:

1. Start by isolating one of the absolute value terms. You can choose either $3|х+2|$ or $2|х+2|$. Let's choose $3|х+2|$:

   $3|х+2|+2|х+2|=5$

   Subtract $2|х+2|$ from both sides:

   $3|х+2|=5-2|х+2|$

2. Now, you have two cases to consider, depending on the sign of $х+2$:

   Case 1: $х+2$ is non-negative ($х+2 \geq 0$):

   In this case, the absolute value becomes unnecessary, so you can rewrite the equation as:

   $3(х+2) = 5-2(х+2)$

   Solve for $x$:

   $3x + 6 = 5 - 2x - 4$

   Combine like terms:

   $3x + 2x + 6 + 4 = 5$

   $5x + 10 = 5$

   Subtract 10 from both sides:

   $5x = -5$

   Divide by 5:

   $x = -1$

   So, $x = -1$ is a solution in this case.

   Case 2: $х+2$ is negative ($х+2 < 0$):

   In this case, the absolute value changes the sign, so you can rewrite the equation as:

   $3-(х+2) = 5-2(х+2)$

   Solve for $x$:

   $3 - x - 2 = 5 - 2x - 4$

   Combine like terms:

   $-x + 1 = -2x + 1$

   Add $x$ to both sides:

   $1 = -x + 1$

   Subtract 1 from both sides:

   $0 = -x$

   Divide by -1 (which is the same as multiplying by -1):

   $0 = x$

   So, $x = 0$ is a solution in this case.

Now you have two potential solutions: $x = -1$ and $x = 0$. You should check both solutions by plugging them back into the original equation to ensure they satisfy it:

For $x = -1$:

$3|(-1)+2|+2|(-1)+2| = 3|1|+2|1+2| = 3(1) + 2(3) = 3 + 6 = 9$

For $x = 0$:

$3|0+2|+2|0+2| = 3|2|+2|2| = 3(2) + 2(2) = 6 + 4 = 10$

Both solutions satisfy the original equation, so the solutions are $x = -1$ and $x = 0$.