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Why are inverse relationships between operations used to solve two step inequalities?

zhenek [66]

Answer:

The goal in solving an equation is to get the variable by itself on one side of the equation and a number on the other side of the equation. To isolate the variable, we must reverse the operations acting on the variable. We do this by performing the inverse of each operation on both sides of the equation.

Reverse addition and subtraction (by subtracting and adding) outside parentheses. Reverse multiplication and division (by dividing and multiplying) outside parentheses. When multiplying or dividing by a negative number, flip the inequality sign. It does not matter if the number being divided is positive or negative

It's necessary to apply inverse operations on both sides of the equals signs so that you can solve for the variable and balance the equation.

Multi-step inequalities are solved using the same processes that work for solving equations with one exception. When you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality symbol. (Much like when you divide by a negative number, the sign of the inequality must flip! Here's why: When you multiply both sides by a negative value you make the side that is greater have a "bigger" negative number, which actually means it is now less than the other side!)

4 0

3 years ago

Express the terms of the following sequence by giving a recursive formula.

emmasim [6.3K]

The recursive formula for given sequence is: $a_n = a_{n-1}-7$

And the terms will be expressed as:

$a_1 = 11\\a_2 = a_{2-1} - 7 \\a_2= a_1 - 7\\a_2 = 11- 7\\a_2 = 4\\a_3 = a_{3-1} - 7 \\a_3= a_2 - 7\\a_3 = 4 - 7\\a_3 = -3\\a_4 = a_{4-1} - 7 \\a_4= a_3 - 7\\ a_4= -3 - 7\\a_4 = -10\\a_5 = a_{5-1} - 7 \\a_5= a_4 - 7\\a_5 = -10 - 7\\a_5 = -17\\$

Step-by-step explanation:

First of all, we have to determine if the given sequence is arithmetic sequence or geometric. For that purpose, we calculate the common difference and common ratio

Given sequence is:

11,4,-3,-10,-17...

Here

$a_1 = 11\\a_2 = 4\\a_3 = -3\\So,\\d = a_2 - a_1 = 4-11 = -7\\d = a_3-a_2 = -3-4 = -7$

As the common difference is same, given sequence is an arithmetic sequence.

A recursive formula is a formula that is used to generate the next term of the sequence using the previous term and common difference

So, the recursive formula for an arithmetic sequence is given by:

$a_n = a_{n-1} +d\\Putting\ d = -7\\a_n = a_{n-1}-7$

Hence,

The recursive formula for given sequence is: $a_n = a_{n-1}-7$

And the terms will be expressed as:

$a_1 = 11\\a_2 = a_{2-1} - 7 \\a_2= a_1 - 7\\a_2 = 11- 7\\a_2 = 4\\a_3 = a_{3-1} - 7 \\a_3= a_2 - 7\\a_3 = 4 - 7\\a_3 = -3\\a_4 = a_{4-1} - 7 \\a_4= a_3 - 7\\ a_4= -3 - 7\\a_4 = -10\\a_5 = a_{5-1} - 7 \\a_5= a_4 - 7\\a_5 = -10 - 7\\a_5 = -17\\$

Keywords: arithmetic sequence, common difference

Learn more about arithmetic sequence at:

#LearnwithBrainly

6 0

4 years ago

Write an absolute value equation with-1 and 5 as the solution.

Dvinal [7]

Answer:

it is detailed solution. please mark brainlest.

Thank you have a nice day