Question

simplify: $0.3(4x - 2) - 0.5(x + 6)$
\text{a. } 0.7x + 2
\text{b. } 1.2x + 1
\text{c. } 1.2x - 6
\text{d. } 0.7x - 3.6

Explanation:

Step1: Distribute the coefficients

First, we distribute \(0.3\) to \((4x - 2)\) and \(-0.5\) to \((x + 6)\).
For \(0.3(4x - 2)\), we use the distributive property \(a(b - c)=ab - ac\). So, \(0.3\times4x = 1.2x\) and \(0.3\times(-2)=-0.6\).
For \(-0.5(x + 6)\), we use the distributive property \(a(b + c)=ab + ac\). So, \(-0.5\times x=-0.5x\) and \(-0.5\times6 = - 3\).
Now the expression becomes: \(1.2x-0.6-0.5x - 3\)

Step2: Combine like terms

Next, we combine the \(x\)-terms and the constant terms.
For the \(x\)-terms: \(1.2x-0.5x=(1.2 - 0.5)x = 0.7x\)
For the constant terms: \(-0.6-3=-3.6\)
Putting it together, the simplified expression is \(0.7x-3.6\)

Answer:

d. \(0.7x - 3.6\)