Question

solve for the following integer:
3(x + 1) - x = 7

a) x = 3
b) x = 2
c) x = -1
d) x = \frac{3}{2}

(options to circle: d, c, a, b)

Explanation:

Step1: Expand the left - hand side

We use the distributive property \(a(b + c)=ab+ac\) to expand \(3(x + 1)\). So \(3(x + 1)-x=3x+3 - x\).

Step2: Combine like terms

Combine the \(x\) terms: \(3x - x+3 = 2x+3\). Now our equation is \(2x + 3=7\).

Step3: Isolate the variable term

Subtract 3 from both sides of the equation: \(2x+3 - 3=7 - 3\), which simplifies to \(2x = 4\).

Step4: Solve for \(x\)

Divide both sides by 2: \(\frac{2x}{2}=\frac{4}{2}\), so \(x = 2\).

Answer:

b) \(x = 2\)