Solve this problem by writing and solving an inequality. 7 more than four times a number is less than -40

Answer 1

Let's define the variable for the unknown number as $x$. The phrase "7 more than four times a number" can be mathematically expressed as:

$$4x+7$$

According to the problem, this expression is less than -40. Therefore, we can set up the inequality:

$$4x+7<-40$$

Now, we will solve the inequality step-by-step.

1. Subtract 7 from both sides:

$$4x<-40-7$$

$$4x<-47$$

2. Now, divide both sides by 4:

$$x<\frac{-47}{4}$$

3. Simplify the fraction:

$$x<-11.75$$

Therefore, the solution to the inequality is:

$$x<-11.75$$

This means that any number less than -11.75 satisfies the original condition.