Question

|2x+5|+3=13.. .........

Answer 1

|2x+5|=10

$\left \{ {{2x+5=10} \atop {2x+5=-10}} \right.$

$\left \{ {{x=\frac{5}{2} } \atop {x=\frac{-15}{2} }} \right.$

x1=-7.5;x2=2.5

Answer 2

To solve the equation |2x + 5| + 3 = 13, you need to isolate the absolute value term and then solve for x. Remember that the absolute value of a number can be either positive or negative, so there may be two possible solutions for x.

Let's proceed with the steps to solve the equation:

Step 1: Get rid of the constant on the right side by subtracting 3 from both sides of the equation:

|2x + 5| = 13 - 3

Simplify:

|2x + 5| = 10

Step 2: Now, split the equation into two separate cases, one for when 2x + 5 is positive and the other for when it's negative:

Case 1: 2x + 5 is positive (2x + 5 ≥ 0):

If 2x + 5 is positive, then the absolute value |2x + 5| will be equal to 2x + 5:

2x + 5 = 10

Step 3: Solve for x in Case 1:

Subtract 5 from both sides:

2x = 10 - 5

2x = 5

Divide both sides by 2:

x = 5 / 2

x = 2.5

Case 2: 2x + 5 is negative (2x + 5 < 0):

If 2x + 5 is negative, then the absolute value |2x + 5| will be equal to its negation:

-(2x + 5) = 10

Step 4: Solve for x in Case 2:

Distribute the negative sign:

-2x - 5 = 10

Add 5 to both sides:

-2x = 10 + 5

-2x = 15

Divide both sides by -2:

x = 15 / -2

x = -7.5

Step 5: Check the solutions:

Plug both solutions back into the original equation to verify:

For x = 2.5:

|2(2.5) + 5| + 3 = |5 + 5| + 3 = |10| + 3 = 10 + 3 = 13 ✓

For x = -7.5:

|2(-7.5) + 5| + 3 = |-15 + 5| + 3 = |-10| + 3 = 10 + 3 = 13 ✓

Both solutions satisfy the original equation, so the two solutions for x are x = 2.5 and x = -7.5.