Question

Evaluate the expressions 3x-2 and 4x+4 for the following value of x.

Answer 1

Question:

Evaluate the expressions 3x - 2 and 4x + 4 for the following values of x. When you have found the value for each expression, write a statement using <, >, or = that shows how the two values are related. a. x = 0 b. x = -6 c. x = 5 d. x = -2

Answer:

Part a: $4x+4>3x-2$

Part b: $4x+4=3x-2$

Part c: $4x+4>3x-2$

Part d: $4x+4>3x-2$

Explanation:

Part a: Substituting $x=0$, we get,

$\begin{aligned}3 x-2 &=3(0)-2 \\&=-2\end{aligned}$

$\begin{aligned}4 x+4 &=4(0)+4 \\&=4\end{aligned}$

The value of $3x-2$ is less than $4x+4$

Thus, $4x+4>3x-2$

Part b: Substituting $x=-6$, we get,

$\begin{aligned}3 x-2 &=3(-6)-2 \\&=-18-2 \\&=-20\end{aligned}$

$\begin{aligned}4 x+4 &=4(-6)+4 \\&=-24+4 \\&=-20\end{aligned}$

The value of $3x-2$ and $4x+4$ are equal.

Thus, $4x+4=3x-2$

Part c: Substituting $x=5$, we get,

$\begin{aligned}3 x-2 &=3(5)-2 \\&=15-2 \\&=13\end{aligned}$

$\begin{aligned}4 x+4 &=4(5)+4 \\&=20+4 \\&=24\end{aligned}$

The value of $3x-2$ is less than $4x+4$

Thus, $4x+4>3x-2$

Part d: Substituting $x=-2$, we get,

$\begin{aligned}3 x-2 &=3(-2)-2 \\&=-6-2 \\&=-8\end{aligned}$

$\begin{aligned}4 x+4 &=4(-2)+4 \\&=-8+4 \\&=-4\end{aligned}$

The value of $3x-2$ is less than $4x+4$

Thus, $4x+4>3x-2$