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Linear Equations and Inequalities

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Linear Equations and Inequalities

Solve equations, rearrange formulae and interpret inequalities to help plan an event. Show working where needed. Give units for measurements.

Solve and check

Isolate the variable using inverse operations. Check by substitution when asked.

1.The event has a $7 booking fee plus $3 per hire. The total is $22. Solve 3h + 7 = 22 to find the number of hires h.

2.A sign-making kit costs $5 to set up, then $2 for each sign. The bill is $31. Solve 2s + 5 = 31 to find the number of signs s.

3.Solve (2m)/3 + 6 = 10. Show how you undo the operations in the correct order.

4.A volunteer claims x = 5 solves 3x + 7 = 22. Substitute x = 5 into the left side and decide whether the claim is correct.

TrueFalse

Formulae in action

Use the event equipment and travel formulae. Include units in your answers.

5.A rectangular banner has area A = lw. Its area is 48 cm² and its length is 8 cm. Substitute the values and find its width w.

6.Travel distance is given by d = vt, where d is distance, v is speed and t is time. Rearrange the formula to make t the subject.

7.A delivery van travels 120 km in 3 hours. Use v = d/t to calculate its average speed.

Inequalities and number lines

Solve each inequality. When asked, show the solution on the number line provided; remember to reverse the inequality sign when multiplying or dividing by a negative number.

8.Entry costs $4 per person, and the group has at most $20 to spend. Write and solve an inequality for the number n of people.

9.Solve 2x − 3 < 5, then mark the solution on the number line.

10.Solve −3x + 1 > 4. Explain why the inequality sign changes, then mark the answer on the number line.

11.A skater must be at least 12 years old and younger than 17. Write the combined inequality and show the eligible ages on the number line.

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About This Worksheet

Free in Kuraplan

Print-Ready

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For Teachers & Parents

Need a custom version of this worksheet?

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