Put it back and check
A solution makes the LHS equal to the RHS. A wrong answer does not.
Is the answer right?
A student solved 2v − 4 = 6 and wrote v = 8. The student has not said how sure they are.
How can we find out if the answer to an equation is right?
What this lesson covers
The idea
A solution is checked by substituting it for the letter-number in the equation and verifying that the LHS equals the RHS.
Is the answer right?
A student solved 2v − 4 = 6 and wrote v = 8. The student has not said how sure they are.
How can we find out if the answer to an equation is right?
- Put it back in the equation
- Solve it again the same way
- Trust the answer if it looks neat
Substitute and compare
For each claim, put the value in place of the letter-number on each side. Work out both sides, then decide: is it a solution?
One check settles it
Put the value back in the original equation. Work out the LHS and the RHS separately. If they match, the value is a solution. If they do not, there was a mistake in the working.
A solution is checked by substituting it for the letter-number in the equation and verifying that the LHS equals the RHS.
- Claim | Check
- 5x − 4 = 7, *x* = 11/5 | LHS 5 × 11/5 − 4 = 7 = RHS ✓
- 6y + 7 = 4y + 21, *y* = 7 | LHS 49, RHS 49 ✓
- 2v − 4 = 6, *v* = 8 | LHS 12, RHS 6 ✗
- 5z + 2 = 3z − 4, *z* = −2 | LHS −8, RHS −10 ✗
Notes
To check a solution, put it in place of the letter-number in the original equation and see that the LHS equals the RHS.
Check yourself
A student says z = 4 solves 3z + 5 = 20. Put 4 in the LHS. What does the LHS come to?
Answer: 17
3 × 4 + 5 = 12 + 5 = 17. It is not 20, so z = 4 is not a solution.
A student solved 4x + 6 = 10 and wrote *x* = 4. Is that right?
Check z = −3 in 5z + 2 = 3z − 4. What does the RHS, 3z − 4, come to?
Answer: -13
3 × (−3) − 4 = −9 − 4 = −13. The LHS is 5 × (−3) + 2 = −13 too, so z = −3 is a solution.
Which is the way to check an answer?
- Yes: 4 × 4 = 16, which is more than 10, so it works.. Working out only 4x is not the check. The whole LHS is 4x + 6, and it must equal 10.
- No: the LHS is 4 × 4 + 6 = 22, but the RHS is 10. — correct. Yes! The sides differ, so x = 4 is not a solution. (The solution is x = 1.)
- Yes, because 4 is in the equation.. A number being in the equation does not make it a solution. Only LHS = RHS does.
- Check that the answer is a whole number.. Solutions can be fractions or negative numbers. 11/5 and −3 are fine.
- Put it in the last line of the working, like 2v = 12.. The working may contain the mistake. Always check in the original equation.
- Put it in the original equation and see if the LHS equals the RHS. — correct. Yes! That tests the answer itself, not the working.