Q44. - Algebra 2

Question

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

One more than product of $-3$ and a number is less than 16.

Step-by-Step Solution

Answer

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

The inequality is: $1+\left(-3\times x\right)<16$

Value of the number is $\text{x}<-\mathbf{5}$

Step 1 - Define the variable.

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

Step 2 - Write the inequality.

From given, let the number multiplied to $-3$ be $x$. 

As one more than the product is less than equal to 16. 

So, the inequality is:

$1+\left(-3\times x\right)<16$

Step 3 - Solve the inequality.

To simplify this inequality, use subtraction property and the division property.

 $\begin{array}{c}1+\left(-3\times x\right)<16\\ 1-3x-1<16-1\\ -3x<15\\ x<-5\end{array}$

Therefore, the inequality is $1+\left(-3\times x\right)<16$ and the value of $x$ is $x<-5$.