Question

1. evaluate the expression 6(x + 4) - 3(x - 2) when

a) x = -10
b) x = -5
c) x = 5
d) x = 10

Explanation:

First, we simplify the expression \(6(x + 4)-3(x - 2)\):

Step 1: Expand the brackets

Using the distributive property \(a(b + c)=ab+ac\), we have:
\(6(x + 4)=6x+24\) and \(-3(x - 2)=-3x + 6\)
So the expression becomes \(6x + 24-3x + 6\)

Step 2: Combine like terms

Combine the \(x\) terms and the constant terms:
\((6x-3x)+(24 + 6)=3x+30\)

Now we evaluate for each value of \(x\):

Part (a): \(x=- 10\)

Step 1: Substitute \(x =-10\) into \(3x + 30\)

Substitute \(x=-10\) into the simplified expression \(3x + 30\)
\(3\times(-10)+30\)

Step 2: Calculate the value

\(3\times(-10)+30=-30 + 30=0\)

Step 1: Substitute \(x=-5\) into \(3x + 30\)

Substitute \(x =-5\) into \(3x+30\)
\(3\times(-5)+30\)

Step 2: Calculate the value

\(3\times(-5)+30=-15 + 30 = 15\)

Answer:

\(0\)

Part (b): \(x=-5\)