Distribute First
About This Worksheet
This worksheet helps ninth-grade students solve multi-step linear inequalities that begin with the distributive property. Each of the eight problems includes parentheses, so students must distribute before they can simplify and isolate x. Some problems also place variable terms on both sides, which means students may need several steps before reaching the final solution. This gives students practice following the correct order instead of trying to solve too quickly.
For example, in an inequality such as 3(x + 4) > 24, students first distribute the 3 to create 3x + 12 > 24. They then subtract 12 and divide to isolate x. More involved problems require students to distribute on both sides before deciding where to move the variable terms.
What Students Practice
Students practice using the distributive property correctly before combining terms or moving variables. They then use inverse operations to isolate x and write the final inequality. This gives them repeated practice with several Algebra 1 skills in one problem.
The worksheet also includes negative coefficients and expressions on both sides of the inequality. Students must watch their signs carefully during distribution and remember to reverse the inequality if they eventually multiply or divide by a negative number. This makes the page a strong step up from basic inequality practice.
Why This Skill Matters
Many linear inequalities are not presented in a ready-to-solve form. Parentheses often need to be removed before students can clearly see the variable and constant terms. Learning to distribute first makes the rest of the solving process much easier to organize.
This skill also carries into equations, functions, and systems. Students use distribution constantly throughout Algebra 1, so becoming accurate with it now is important. Combining that skill with inequality rules helps prepare them for more complex algebra.
Common Challenges
Students may distribute to the first term inside parentheses but forget the second term. Remind them that the outside factor must multiply every term inside the parentheses. Drawing small arrows from the outside number to both terms can help.
Another common mistake is reversing the inequality symbol during distribution simply because the outside factor is negative. The sign reverses only if students actually multiply or divide both sides of the inequality by a negative number as an equation-solving step. Encourage them to simplify first and check the final isolation step carefully.
How To Use It
Teachers can use this worksheet after students understand basic multi-step inequalities and the distributive property separately. It works well for guided practice, independent work, homework, or review before more advanced variable-on-both-sides problems. Modeling one problem with positive distribution and one with negative distribution can help students compare the processes.
Parents and homeschool teachers can ask, “What needs to happen before we can solve for x?” If parentheses are present, distribute first and simplify each side. Then continue using the same inverse-operation steps students already know.
Grade Alignment
This worksheet is designed for Grade 9 Algebra 1 and supports CCSS HSA-REI.B.3, which includes solving linear inequalities in one variable. It also reinforces HSA-SSE.A.1 through understanding and simplifying algebraic expressions. The distributive-property focus helps students solve inequalities that are not initially written in a simple form.
Students should already understand basic distribution and one- or two-step inequalities. After this practice, they can move into more complicated inequalities with several variable terms on both sides.