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Verifying Equation Solutions

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Verifying Equation Solutions

Substitute a proposed value for the variable, evaluate both sides, and decide whether the equation is true. Show your working when asked.

Check each proposed value

Choose whether the proposed value makes the equation true. Substitute it into the equation to check.

1.For 4x + 3 = 19, decide whether x = 4 is a solution.

Yes, it is a solution.
No, it is not a solution.

2.For 3x − 5 = 16, decide whether x = 7 is a solution.

Yes, it is a solution.
No, it is not a solution.

3.For 18 − 2x = 8, decide whether x = 6 is a solution.

Yes, it is a solution.
No, it is not a solution.

4.For 5x + 2 = 27, decide whether x = 5 is a solution.

Yes, it is a solution.
No, it is not a solution.

Match and calculate

Match each equation and proposed value to the result of substituting that value. Use each result once.

5.Match each substitution to its result.

2x + 7 = 17, with x = 5
4x − 3 = 13, with x = 3
20 − 3x = 11, with x = 3
6 + x = 15, with x = 8

Left side is 9; right side is 13
Left side is 14; right side is 15
Both sides equal 17
Both sides equal 11

Show how you know

Write the substitution and compare the value of each side.

6.Check whether x = 4 solves 7x − 6 = 22. Show the value of the left side and state whether it equals the right side.

7.A student says x = 3 solves 5x + 4 = 18. Verify the claim by substituting 3, then explain what the calculation shows.

8.A café order is charged using the rule C = 4n + 3, where n is the number of muffins and C is the total cost in dollars. For an order of 5 muffins, a customer expects to pay $23. Use the rule to check whether the expected total is correct.

9.For 8x + 1 = 41, check whether x = 6 is a solution. Write a line of working and give a conclusion.