CCSS 7.EE.B.4b · solve, graph & interpret inequalities
Practice the full 7.EE.B.4b job rather than stopping at an algebraic answer. Problems solve a one-variable inequality, graph the solution set with an open boundary point, and interpret the allowed values; challenge mode can require reversing the sign after division by a negative coefficient.
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Solve & graph inequalities · Grade 7 standard · Seed 271801
A field trip has a fixed $2 fee plus $8 per student. To keep the total below $26, what numbers of students x are possible? Write, solve, graph, and interpret the inequality.
Solve first, then place an open circle at the boundary and shade the correct direction.
A fundraiser starts with $17 and earns $7 per sale. To raise more than $101, what values of x are possible? Write, solve, graph, and interpret the inequality.
Solve first, then place an open circle at the boundary and shade the correct direction.
A fundraiser starts with $18 and earns $8 per sale. To raise more than $58, what values of x are possible? Write, solve, graph, and interpret the inequality.
Solve first, then place an open circle at the boundary and shade the correct direction.
Solve and graph: 2x - 12 < 6
Solve first, then place an open circle at the boundary and shade the correct direction.
Solve and graph: 6x + 4 > -8
Solve first, then place an open circle at the boundary and shade the correct direction.
Solve and graph: 5/2x - 2 > 13
Solve first, then place an open circle at the boundary and shade the correct direction.
A field trip has a fixed $13 fee plus $3 per student. To keep the total below $25, what numbers of students x are possible? Write, solve, graph, and interpret the inequality.
Solve first, then place an open circle at the boundary and shade the correct direction.
Solve and graph: 1/2x + 11 > 43/4
Solve first, then place an open circle at the boundary and shade the correct direction.
A field trip has a fixed $24 fee plus $2 per student. To keep the total below $40, what numbers of students x are possible? Write, solve, graph, and interpret the inequality.
Solve first, then place an open circle at the boundary and shade the correct direction.
Solve and graph: 4x + 1/2 < -71/2
Solve first, then place an open circle at the boundary and shade the correct direction.
Solve an inequality like an equation, with one important change: when you multiply or divide both sides by a negative number, flip the direction of the inequality sign. Then graph the solution on a number line, using an open circle for < or > and a closed circle for ≤ or ≥, and shade in the direction of the solutions.
Ask students to pick one number from their shaded region and substitute it into the original inequality. The answer key shows the solution and the graph, so both can be checked.
A practical match for the skill this worksheet practises, not a claim that one worksheet teaches or assesses the whole standard. Check the official math standards.
A strict < or > inequality uses an open circle because the boundary value is not included.
Dividing or multiplying both sides by a negative number reverses the inequality sign; adding or subtracting a negative does not.
Example: -2x + 5 > 11 gives -2x > 6, then dividing by -2 flips the sign to x < -3, graphed with an open circle at -3 and shading to the left.
In context, translate the graph back into the units of the problem instead of reporting only x < a or x > a.
Continue the 7.EE progression
Yes. Student versions include a clean number line for graphing; the checked view and answer key add the exact open-circle boundary and solution ray as vector graphics.
The focused Grade 7 standard names inequalities of the forms px + q > r and px + q < r, so this generator stays with strict inequalities.