Equations and relationships
Try these fresh problems without your notes. Explain your method before opening a solution. This practice is not a graded school assessment.
Check 1
Solve 0.5x = 6.
Check 2
Which number-line description represents t > −1?
Challenge 1
A taxi model uses C = 3d + 4 dollars for distance d km. Make a table for d = 0, 2, 5. Is the cost directly proportional to distance?
Show a hint
Substitute each distance and consider the fixed charge at zero.
Show the worked solution
Costs $4, $10, $19. The cost is not directly proportional to distance.
There is a $4 fixed charge, so C/d is not constant and the graph does not pass through the origin. Distance is the model input and cost its output.
Challenge 2
A student has $18 and needs $25. Write and solve an equation for the additional amount x. Then write the condition for having more than $25 in total.
Show a hint
For equality use 18 + x = 25; for more than use a strict inequality.
Show the worked solution
18 + x = 25 gives x = 7. More than $25 requires x > 7.
Subtracting eighteen gives the boundary seven. Exactly seven reaches $25, so a strict condition excludes that value.
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