Question

Define a variable and write an inequality for each problem and then solve.

42. The product of a $-4$and a number is at least 35.

Short answer

The inequality is:$-\mathbf{4}\times \text{x}\ge \mathbf{35}$

Value of the number is $\text{x}\ge -\mathbf{8}.\mathbf{75}$

Step-by-step solution

- Define the variable.

A variable is a term that is used to represent an unknown value.

- Write the inequality.

From given, let the number multiplied to $-4$ be $x$.

As the product is at least 35.

So, the inequality is:

$-4\times x\ge 35$

- Solve the inequality.

Simplify the inequality as shown below:

$\begin{array}{c}-4\times x\ge 35\\ x\ge -\frac{35}{4}\\ x\ge -8.75\end{array}$

Therefore, the inequality is $-4\times x\ge 35$ and the value of $x$ is $x\ge -8.75$.