Let's solve the equation [tex]\(3.2x - 1.7x + 5.5 = 10\)[/tex] step-by-step.
### Step 1: Combine Like Terms
First, we need to combine the like terms on the left-hand side of the equation. The like terms involving the variable [tex]\(x\)[/tex] are [tex]\(3.2x\)[/tex] and [tex]\(-1.7x\)[/tex].
[tex]\[ 3.2x - 1.7x = (3.2 - 1.7)x \][/tex]
Calculating the numerical coefficient:
[tex]\[ 3.2 - 1.7 = 1.5 \][/tex]
So, the equation simplifies to:
[tex]\[ 1.5x + 5.5 = 10 \][/tex]
### Step 2: Isolate the Variable Term
Next, we want to isolate [tex]\(x\)[/tex]. To do this, we first need to move the constant term (5.5) to the right-hand side by subtracting 5.5 from both sides of the equation.
[tex]\[ 1.5x + 5.5 - 5.5 = 10 - 5.5 \][/tex]
This simplifies to:
[tex]\[ 1.5x = 4.5 \][/tex]
### Step 3: Solve for [tex]\(x\)[/tex]
To solve for [tex]\(x\)[/tex], we need to divide both sides of the equation by the coefficient of [tex]\(x\)[/tex], which is 1.5.
[tex]\[ x = \frac{4.5}{1.5} \][/tex]
Calculating the division:
[tex]\[ x = 3.0 \][/tex]
### Conclusion
The solution to the equation [tex]\(3.2x - 1.7x + 5.5 = 10\)[/tex] is [tex]\(x = 3.0\)[/tex].
