Question

Write the inequality modeled by the algebra tiles. Then solve the inequality using algebra tiles. Check your answer using properties of inequality.

Answer 1

Step 1 : Form the inequality.

Given:

Let minus sign indicates $-1$ and green plus sign indicates $x$ and yellow plus sign indicates $1$.

We have, $x+1+1+x+1+1\ge -1–1-1-1-1-1$
$\Rightarrow 2x+4\ge -6$, this the required inequality

Step 2 : Solve the inequality

We have, $2x+4\ge -6$

$\Rightarrow 2x\ge -6–4$ [ Subtract $4$ from both sides ]
$\Rightarrow 2x\ge -10$

$\Rightarrow x\ge \frac{-10}{2}$ [ Divide both sides by$2$]
$\therefore x\ge -5$

Hence, the required inequality is $2x+4\ge -6$ and the required solution is $x\ge -5$

Step 3 : Check answer using properties of inequality.

Using subtraction property,

For all real numbers

Here,

$$\begin{gathered} 2x+4\ge -6 \\ \Rightarrow 2x+4-4\ge -6-4 \\ \Rightarrow 2x\ge -10 \\ \Rightarrow x\ge -5 \end{gathered}$$

Hence, it is verified.