To solve the equation ∣2x+5∣+2=5, we first isolate the absolute value expression by subtracting 2 from both sides. This gives us ∣2x+5∣=3. The absolute value equation ∣A∣=B can be split into two separate equations: A=B and A=−B. Therefore, we solve the two equations 2x+5=3 and 2x+5=−3 to find the possible values of x.
Step 1: Isolate the Absolute Value Expression
Start with the equation:
∣2x+5∣+2=5
Subtract 2 from both sides to isolate the absolute value:
∣2x+5∣=3
Step 2: Solve the Absolute Value Equation
The equation ∣A∣=B can be split into two separate equations: A=B and A=−B. Therefore, we have:
2x+5=3
2x+5=−3
Step 3: Solve Each Equation
Solve the first equation:
2x+5=3
Subtract 5 from both sides:
2x=−2
Divide by 2:
x=−1
Solve the second equation:
2x+5=−3
Subtract 5 from both sides:
2x=−8
Divide by 2:
x=−4