Question

Define a variable, write an inequality, and solve each problem. Check your solution.

A number decreased by 4 is more than$-1$.

Short answer

The variable is x is and the inequality equation is $x-4>-1$. The solution for the inequality is $x>3$.

Step-by-step solution

Step 1. State the concept for inequality.

To graph the endpoint with strict inequality < or >, use the open parenthesis or a hollow circle at that endpoint.

To graph the endpoint with inequality symbol $\le \text{or}\ge$, use the bracket or a solid circle at that endpoint.

Properties of inequality:

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Step 2. Write the inequality for the given condition.

Let the number be x.

A number decreased by 4 is more than $-1$:

$x-4>-1$

Step 3. Solve for x.

Solve for x in the inequation$x-4>-1$

$$\begin{gathered} x-4>-1 \\ x-4+4>-1+4 \\ x>3 \end{gathered}$$

Step 4. Check the solution when x=5.

Put the value of xas 5.

$$\begin{gathered} x-4>-1 \\ 5-4>-1 \\ 1>-1\left[\text{TrueStatement}\right] \end{gathered}$$

Thus, the solution of the inequality equation $x-4>-1$is $x>3$.