Question

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

\( x = 1 \)