Term Combine
About This Worksheet
This worksheet helps ninth-grade students solve linear inequalities by combining like terms before isolating the variable. Each of the eight problems includes multiple x-terms, constant terms, or expressions that need to be simplified before the inequality can be solved. Some problems also have variables on both sides, so students must first clean up the expressions and then decide where to collect the variable terms. This gives students practice seeing simplification as an important first step.
For example, an inequality such as 3x + 5x – 6 > 18 should first become 8x – 6 > 18. Students can then add 6 and divide by 8 to solve for x. More complex problems may require like terms to be combined on both sides before the final solving steps begin.
What Students Practice
Students practice identifying terms that have the same variable part and combining their coefficients correctly. They also combine constant terms where possible before using inverse operations. This helps students reduce a busy-looking inequality into a simpler one.
The worksheet also reinforces moving variable terms to one side when needed. Students must keep track of positive and negative coefficients and decide how to create the cleanest path toward isolating x. That builds stronger algebra organization.
Why This Skill Matters
Combining like terms is one of the most basic tools students use to simplify algebraic expressions. If students skip that step or combine unlike terms, the rest of the inequality will usually be wrong. This worksheet gives them focused practice using simplification before solving.
The skill also appears in nearly every later algebra topic. Equations, systems, polynomials, and functions all require students to recognize and combine like terms accurately. Strong habits here make those topics easier to manage.
Common Challenges
Students may try to combine terms that are not actually alike. A term with x can combine with another x-term, but it cannot combine directly with a constant. Encourage students to group variable terms and constants separately before doing arithmetic.
Another common mistake is losing a negative sign while combining coefficients. Remind students that -4x + 3x becomes -x, not x. Writing the coefficients as a quick integer calculation can make these combinations easier.
How To Use It
Teachers can use this worksheet as focused practice after students have already learned how to solve simpler inequalities. It works well for guided review, independent work, homework, or intervention with students who need more practice simplifying expressions. You might ask students to draw a box around like terms before combining them.
Parents and homeschool teachers can ask, “Which terms can be put together before we solve?” Have the student simplify the variable terms and constants first. Once the expression is cleaner, the remaining inequality steps should feel much more familiar.
Grade Alignment
This Grade 9 worksheet supports CCSS HSA-REI.B.3 through solving linear inequalities in one variable. It also reinforces HSA-SSE.A.1, which asks students to interpret and work with the structure of algebraic expressions. Combining like terms accurately is an important part of both skills.
Students should already understand coefficients, constants, and basic inequality solving. After this practice, they can move into longer problems involving distribution and variables on both sides.