Solve the equation 2|2x +3|=10

Question

.(2 points)
x =

or x=

Put the smaller x in the first box

Answer 1

To solve the equation \( 2|2x + 3| = 10 \), we first divide both sides by 2:

\[ |2x + 3| = 5 \]

Next, we can set up two cases based on the absolute value.

Case 1: \( 2x + 3 = 5 \)

Solving this gives:

\[ 2x = 5 - 3 \] \[ 2x = 2 \] \[ x = 1 \]

Case 2: \( 2x + 3 = -5 \)

Solving this gives:

\[ 2x = -5 - 3 \] \[ 2x = -8 \] \[ x = -4 \]

Thus, the solutions for the equation are \( x = 1 \) and \( x = -4 \).

Putting the smaller value first, we have:

\( x = -4 \)

or

\( x = 1 \)