Linear inequalities and simultaneous equations

Solve x + 7 < 12.

Solve 3x - 5 ≥ 10.

Explain what happens to an inequality sign when both sides are multiplied by -1.

Solve -2x < 8.

Write the solution x ≥ 4 in words.

Check whether x = 3 satisfies 2x + 1 > 8.

Solve the simultaneous equations x + y = 9 and x - y = 1.

State what the intersection point of two straight-line graphs represents.

Correct this error: dividing -6x < 12 by -6 gives x < -2.

Give one real context that could be modelled by simultaneous equations.

Solve 4x - 7 ≤ 17 and represent the solution on a number line.

Solve -3(x - 2) > 12, explaining every inequality step clearly.

Solve the system 2x + y = 11 and x - y = 1 using elimination.

Solve the system y = 2x + 3 and y = -x + 12 using substitution.

A movie ticket and snack cost $18. Two tickets and one snack cost $30. Form and solve simultaneous equations to find each cost.

Graph or describe how you would solve y = x + 2 and y = -2x + 8, and interpret the intersection.

Create a worded constraint that can be represented by x + y ≤ 20 and explain what values make sense.

Compare solving a simultaneous system by graphing, substitution and elimination. State when each method is useful.

A student solves 5 - 2x ≥ 13 and forgets to reverse the inequality. Find and correct the error.

Write a full modelling problem involving two unknowns, form simultaneous equations, solve them and check the answer in context.