To solve the equation [tex]\( x - 3x + 7 = x + 2 \)[/tex], let's go through each step systematically:
### Step 1: Simplify the equation
First, combine like terms on the left-hand side:
[tex]\[ x - 3x + 7 = x + 2 \][/tex]
[tex]\[ -2x + 7 = x + 2 \][/tex]
### Step 2: Isolate the variable [tex]\( x \)[/tex] on one side
To isolate [tex]\( x \)[/tex] on one side, subtract [tex]\( x \)[/tex] from both sides of the equation:
[tex]\[ -2x + 7 - x = x + 2 - x \][/tex]
[tex]\[ -3x + 7 = 2 \][/tex]
### Step 3: Solve for [tex]\( x \)[/tex]
Next, isolate [tex]\( x \)[/tex] by moving the constant term to the right-hand side. Subtract 7 from both sides:
[tex]\[ -3x + 7 - 7 = 2 - 7 \][/tex]
[tex]\[ -3x = -5 \][/tex]
Now, divide both sides by -3 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{-5}{-3} \][/tex]
[tex]\[ x = \frac{5}{3} \][/tex]
### Final Answer:
The solution to the equation [tex]\( x - 3x + 7 = x + 2 \)[/tex] is [tex]\( x = \frac{5}{3} \)[/tex].
This means that the value [tex]\( x \)[/tex] which satisfies the given equation is [tex]\( \frac{5}{3} \)[/tex].
