Question

How many solutions does this equation have?
5(2x
+
4)
=
7x
+
3x
+ 4
10x
+
20
=
7x
+
3x
+ 4
10x
+
20
=
10x
+ 4

There are infinitely many solutions to this equation.

There are no solutions to this equation.

There is no way to know how many solutions there are yet.

Answer 1

To solve the equation:

\[
5(2x + 4) = 7x + 3x + 4
\]

First, simplify both sides.

The left side:
\[
5(2x + 4) = 10x + 20
\]

The right side:
\[
7x + 3x + 4 = 10x + 4
\]

Now the equation looks like:
\[
10x + 20 = 10x + 4
\]

Next, we can simplify this:

Subtract \(10x\) from both sides:
\[
20 = 4
\]

This statement is false and shows a contradiction. Since there's no value of \(x\) that can satisfy this equation, we conclude that:

**There are no solutions to this equation.**