Questions: Solve for (x) : [ 2 x+5+2=5 x= ]

Solve for (x) :
[
2 x+5+2=5 
x=
]
Transcript text: Solve for $x$ : \[ \begin{array}{l} |2 x+5|+2=5 \\ x= \end{array} \]
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Solution

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Solution Steps

To solve the equation 2x+5+2=5|2x + 5| + 2 = 5, we first isolate the absolute value expression by subtracting 2 from both sides. This gives us 2x+5=3|2x + 5| = 3. The absolute value equation A=B|A| = B can be split into two separate equations: A=BA = B and A=BA = -B. Therefore, we solve the two equations 2x+5=32x + 5 = 3 and 2x+5=32x + 5 = -3 to find the possible values of xx.

Step 1: Isolate the Absolute Value Expression

Start with the equation: 2x+5+2=5 |2x + 5| + 2 = 5 Subtract 2 from both sides to isolate the absolute value: 2x+5=3 |2x + 5| = 3

Step 2: Solve the Absolute Value Equation

The equation A=B|A| = B can be split into two separate equations: A=BA = B and A=BA = -B. Therefore, we have:

  1. 2x+5=32x + 5 = 3
  2. 2x+5=32x + 5 = -3
Step 3: Solve Each Equation

Solve the first equation: 2x+5=3 2x + 5 = 3 Subtract 5 from both sides: 2x=2 2x = -2 Divide by 2: x=1 x = -1

Solve the second equation: 2x+5=3 2x + 5 = -3 Subtract 5 from both sides: 2x=8 2x = -8 Divide by 2: x=4 x = -4

Final Answer

x=1,4\boxed{x = -1, -4}

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