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Equation Solving Strategies

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Equation Solving Strategies

Solve each equation by undoing the operations in reverse order. Show your working and check each solution by substituting it into the original equation.

Solve and Check

1.Solve x + 8 = 19. Show your working, then check your value of x by substitution.

2.Solve 6a = 42. Show the inverse operation you use and check your answer.

3.Solve 4p + 3 = 27. Write each step clearly.

4.Solve 5b − 6 = 24. Write each step clearly.

5.Which equation is true when t = 5?

3t + 2 = 17
4t − 3 = 15
t + 8 = 12
6t = 25

Equations in Everyday Situations

6.Oliver has $38 saved and wants to have $95. Let m be the amount, in dollars, she still needs to save. Write an equation and solve for m.

7.Each entry to a skating rink costs $9. A group also pays a one-off equipment hire fee of $6. Their total bill is $60. If n is the number of entries, write an equation and find n.

8.At dawn, the temperature was t °C. It fell by 7°C and later measured 12°C. Write an equation and work out the temperature at dawn.

Patterns and Puzzles

9.A pattern has value 4 at position 1, value 7 at position 2, value 10 at position 3, and value 13 at position 4. The value increases by the same amount each time. Write a rule for the value V at position n, then use it to find the value at position 12.

10.A number is multiplied by 4, then 5 is added. The result is 33. Write an equation and solve to find the number.

11.Explain how you would solve 3x + 8 = 29. State which operation you undo first and how you find x.