Which value makes it true? worksheets

An equation is a question, and a solution is a number that makes it a true sentence. These free printable worksheets hand over the sentence and the candidates and ask which one works — no solving allowed, just substitution.

Which value makes it true?
Which value makes it true? worksheet — Equations and inequalities, values to 11, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

Solving an equation is a set of moves, and a student can learn the moves without ever believing what they are for. This page asks the question underneath them: 4x + 3 = 19 is not an instruction, it is a sentence that is true for one value of x and false for every other, and putting a number in is how you find out which. Every question here is answered by substitution and nothing else.

Why this sheet works

The inequality half is what makes the idea necessary. An equation has one answer, so a student can reach it by solving and never test anything. 3x + 1 > 10 has infinitely many, so there is no answer to reach for — there is only a test that each candidate passes or fails, which is exactly what the standard describes. The candidates always straddle the boundary, and the boundary value itself is always offered, because "is 3 more than 3" is the step that gets skipped.

How this one works

Try each value and see which one works

6789
x = 66 × 6 + 8= 44
44=56false
x = 76 × 7 + 8= 50
50=56false
x = 86 × 8 + 8= 56
56=56true
x = 8
  1. 6x + 8 = 56 is a sentence, not an instruction. It is true for one of these values and false for the others, and the way to find out is to try them.
  2. Try x = 6. 6 × 6 + 8 = 44. 44 is not 56, so x = 6 does not work.
  3. Try x = 7. 6 × 7 + 8 = 50. 50 is not 56, so x = 7 does not work.
  4. Try x = 8. 6 × 8 + 8 = 56. 56 really is 56, so x = 8 makes it true.
  5. Only one value out of the four turns the sentence into something true, and that is what a solution is.