Watch with Theo · Answer choices
ACT Math: Work Backward from the Answer Choices
Test possible values in the original equation and check that they meet every condition.
Take this into your next practice session
Choose between substitution and direct algebra. Back solving is a tool, not a requirement.
Choose an answer, then check your reasoning. This public practice is not saved.
Read all answer explanations
5: Substitute your choice for x, multiply by 5, then subtract 4. You need a result of 31.
6: Substitute your choice for x, multiply by 5, then subtract 4. You need a result of 31.
7 — correct answer: Correct. 5(7) − 4 = 35 − 4 = 31. Both sides match.
8: Substitute your choice for x, multiply by 5, then subtract 4. You need a result of 31.
Full transcript and worked example
Work backward from the choices.
Hi, I'm Theo. Sometimes the answer choices can help you solve a problem. Here we need x, and the choices are possible values. We can test them in the original equation.
4x + 7 = 35
Try one value.
Try six. Four times six plus seven is thirty one. That is too small. In this equation, increasing x increases the left side, so try a larger choice.
If x = 6: 4(6) + 7 = 31
Check the next choice.
Try seven. Four times seven plus seven equals thirty five. That matches the right side. Seven works.
If x = 7: 4(7) + 7 = 35
Know when this method applies.
You could also subtract seven and divide by four. Choose the method you find clearer. Back solving helps when choices are possible values, but always check the original conditions. More complicated equations can have several solutions.
4x = 28 → x = 7
Test the original statement.
Now try five x minus four equals thirty one. Test a choice in the original equation, or solve directly. Either way, finish by checking that both sides match.
5x − 4 = 31
Keep learning
Original Raise Your ACT content, independent of ACT. How we review content.