Sure! Let's solve the equation step by step:
The given equation is:
[tex]\[ 2(2x - 5) = 3x + x - 2x \][/tex]
1. First, simplify both sides of the equation.
Expanding the left side:
[tex]\[ 2(2x - 5) = 2 \cdot 2x - 2 \cdot 5 = 4x - 10 \][/tex]
Simplifying the right side:
[tex]\[ 3x + x - 2x = (3 + 1 - 2)x = 2x \][/tex]
So the equation now looks like:
[tex]\[ 4x - 10 = 2x \][/tex]
2. Next, let's get all terms containing [tex]\( x \)[/tex] on one side of the equation and the constants on the other side. Subtract [tex]\( 2x \)[/tex] from both sides:
[tex]\[ 4x - 10 - 2x = 2x - 2x \][/tex]
[tex]\[ 2x - 10 = 0 \][/tex]
3. Now, isolate [tex]\( x \)[/tex] by adding 10 to both sides:
[tex]\[ 2x - 10 + 10 = 0 + 10 \][/tex]
[tex]\[ 2x = 10 \][/tex]
4. Lastly, solve for [tex]\( x \)[/tex] by dividing both sides by 2:
[tex]\[ \frac{2x}{2} = \frac{10}{2} \][/tex]
[tex]\[ x = 5 \][/tex]
So, the solution to the equation [tex]\( 2(2x - 5) = 3x + x - 2x \)[/tex] is:
[tex]\[ x = 5 \][/tex]
