Question

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

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

Explanation:

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

Step 1: Expand the expression

Using the distributive property \(a(b + c)=ab+ac\), we have:
\(6x + 3(x + 4)=6x+3x + 12\)

Step 2: Combine like terms

Combine the \(x\) terms:
\(6x+3x + 12=(6 + 3)x+12=9x + 12\)

Now we evaluate the simplified expression \(9x + 12\) for each value of \(x\):

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

Step 1: Substitute \(x =-10\) into \(9x + 12\)

\(9\times(-10)+12\)

Step 2: Perform the multiplication

\(9\times(-10)=-90\)

Step 3: Perform the addition

\(-90 + 12=-78\)

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

Step 1: Substitute \(x=-5\) into \(9x + 12\)

\(9\times(-5)+12\)

Step 2: Perform the multiplication

\(9\times(-5)=-45\)

Step 3: Perform the addition

\(-45 + 12=-33\)

Part (c): When \(x = 5\)

Step 1: Substitute \(x = 5\) into \(9x+12\)

\(9\times5+12\)

Step 2: Perform the multiplication

\(9\times5 = 45\)

Step 3: Perform the addition

\(45+12=57\)

Part (d): When \(x = 10\)

Step 1: Substitute \(x = 10\) into \(9x + 12\)

\(9\times10+12\)

Step 2: Perform the multiplication

\(9\times10=90\)

Step 3: Perform the addition

\(90+12 = 102\)

Answer:

s:
a) \(-78\)

b) \(-33\)

c) \(57\)

d) \(102\)