How many solutions does this equation have?

Question

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.