Question

expressions 5

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 the simplified expression \(3x + 30\) for each value of \(x\):

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

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

\(3(-10)+30\)

Step 2: Calculate the value

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

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

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

\(3(-5)+30\)

Step 2: Calculate the value

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

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

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

\(3(5)+30\)

Step 2: Calculate the value

\(3\times5 = 15\), then \(15+30=45\)

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

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

\(3(10)+30\)

Step 2: Calculate the value

\(3\times10=30\), then \(30 + 30=60\)

Answer:

s:
a) \(\boldsymbol{0}\)

b) \(\boldsymbol{15}\)

c) \(\boldsymbol{45}\)

d) \(\boldsymbol{60}\)