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 : According to given algebra tiles:

Let minus sign indicates $-x$ and plus sign indicates $1$

We have,

$-x+1-x+1>+1+1+1+1+1+1$
$\Rightarrow -2x+2>6$ , this the required inequality

Step 2 : Solve the inequality

We have,

$\Rightarrow -2x+2>6$

$\Rightarrow -2x+2-2>6–2$ [ Subtract $2$ from both sides ]
$$\begin{gathered} \Rightarrow -2x+2-2>6–2 \\ \Rightarrow -2x>4 \end{gathered}$$

$\Rightarrow x<\frac{4}{-2}$ [ Divide by $-2$ both sides and reverse the inequality ]
$\therefore x<-2$

Hence, the required inequality is $-2x+2>6$ and the required solution is $x<-2$

Step 3 : Check answer using properties of inequality:

Using subtraction property,

For all real numbers

Here,

$$\begin{gathered} -2x+2>6 \\ -2x+2-2>6-2 \\ -2x>4 \\ x<-2 \end{gathered}$$

Hence, it is verified.