Solving two step inequalities worksheet with answers

Example 1 : 

Sum of two times of a number and 5 is less than -11. Find the number.

Solution :

Let x be the number.

Step 1 : 

Write the inequality.

2x + 5 < -11

Step 2 :

Solve the inequality using Subtraction and Division properties of Inequality.

Subtract 5 on from both sides. 

(2x + 5) - 5 < -11 - 5

2x < -16

Divide both sides by 2

(2x) / 2 < (-16) / 2

x < -8

So, the number is any value less than -8. 

Example 2 : 

A mountain climbing team is camped at an altitude of 18,460 feet on Mount Everest. The team wants to reach more than 29,029-foot summit within 6 days. Find the average number of feet per day the team must climb to accomplish its objective.

Solution :

Let x be the average number of feet per day the team must climb to accomplish its objective. 

Step 1 : 

Write the inequality.

6x + 18460 ≥ 29029

Step 2 :

Solve the inequality using Subtraction and Division properties of Inequality.

Subtract 18460 on from both sides. 

(6x + 18460) - 18460 ≥ 29029 - 18460

6x ≥ 10569

Divide both sides by 6

(6x) / 6 ≥ (10569) / 6

x ≥  1761.5

So, the team must climb at least 1761.5 feet per day to accomplish its objective.

Example 3 : 

The 45 members of the glee club are trying to raise more than $6,000, so they can compete in the state championship. They already have $1,230. Find the amount that each member must raise, on average, to meet the goal?

Solution :

Let x be the amount that each member must raise on average to meet the goal.  

Step 1 : 

Write the inequality.

45x + 1230 ≥ 6000

Step 2 :

Solve the inequality using Subtraction and Division properties of Inequality.

Subtract 1230 on from both sides. 

(45x + 1230) - 1230 ≥ 6000 - 1230

45x ≥ 4770

Divide both sides by 45

(45x) / 45 ≥ (4770) / 45

x ≥ 106

So, each member must raise at least $106 on average to meet the goal

Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

Kindly mail your feedback to 

We always appreciate your feedback.

©All rights reserved. onlinemath4all.com

At the heart of our free printable two-step inequalities worksheets is a golden opportunity for children to practice and master solving and graphing two-step inequalities with a precision like never before. Through these pdfs, the young learners will have to exercise care while applying inverse operations such as additive inverse and multiplicative inverse to isolate the variable and then solve the inequalities with expertise.

Our two-step inequalities worksheets are suitable for students in grade 7, grade 8, and high school.

CCSS: 7.EE

Solving Two-Step Inequalities | Integers | Worksheet #1

Excel your peers by getting the variable isolated on one side after performing inverse operations on either side. First, you must work your way around constants and coefficients and then solve the two-step inequalities.

Solving Two-Step Inequalities | Integers | Worksheet #2

This pdf, a key aspect of our free solving two-step inequalities worksheets for 7th grade and 8th grade, readily delivers a set of ten moderately easy exercises involving two-step inequalities with integer coefficients.

Solving Two-Step Inequalities | Fractions

With fractional constants and fractional coefficients, this worksheet unravels a diverse layer of the topic! Guide children to eliminate the constants and then the coefficients in order to solve the two-step inequalities.

Graphing Two-Step Inequalities | Worksheet #1

For the active learners who wish to nail graphing two-step inequalities correctly, this free printable leads them to solve the inequalities and ensure that the graph they're making satisfies the solution.

Graphing Two-Step Inequalities | Worksheet #2

Make this graphing two-step inequalities worksheet a compulsory part of grade 7 and grade 8 children's practice regime! Shoehorn abundant practice in solving 2-step inequalities with two operations.

Identifying the Graph of Two-Step Inequality

Is the child equipped to identify the graph of 2-step inequalities accurately? Test them with this free identifying the graph of two-step inequality worksheet where students select from four graphs that describe each two-step inequality.

Identifying Two-Step Inequality That Describes the Graph

Let everything be easy and crystal-clear for 8th grade and high school students! This section of our solving two-step inequalities worksheets drives them to identify the appropriate inequality that describes the given graph.

How do you solve two step inequalities?