Let's solve the equation step by step to find the value of [tex]\( x \)[/tex].
The original equation is:
[tex]\[ 0.5x + 4 + 0.9x = x + 5 \][/tex]
1. Combine like terms on the left side of the equation:
[tex]\[ 0.5x + 0.9x + 4 = x + 5 \][/tex]
2. Simplify the like terms:
[tex]\[ 1.4x + 4 = x + 5 \][/tex]
3. Move all terms involving [tex]\( x \)[/tex] to one side of the equation. Subtract [tex]\( x \)[/tex] from both sides:
[tex]\[ 1.4x - x + 4 = 5 \][/tex]
4. Simplify the equation:
[tex]\[ 0.4x + 4 = 5 \][/tex]
5. Isolate [tex]\( x \)[/tex] by subtracting 4 from both sides:
[tex]\[ 0.4x = 1 \][/tex]
6. Solve for [tex]\( x \)[/tex] by dividing both sides by 0.4:
[tex]\[ x = \frac{1}{0.4} \][/tex]
7. Simplify the division:
[tex]\[ x = 2.5 \][/tex]
Thus, the solution for [tex]\( x \)[/tex] is:
[tex]\[ x = 2.5 \][/tex]
Therefore, the correct answer is:
A. [tex]\( x = 2.5 \)[/tex]
