Free sample · Sec 1

Check a linear equation

solving a linear equation and substituting to reject a tempting wrong root.

Sec 1 · Logic · Sec 1 · Angles · A-Math sample

I Do

Worked example

Solve $2 (x - 3) = 10$ .

A common wrong move is to drop the brackets badly and write $2 x - 3 = 10$ , which gives $x = 6.5$ — or to ignore the 2 and write $x - 3 = 10$ , which gives $x = 13$ .

Try $x = 13$ : $2 (13 - 3) = 2 \times 10 = 20$ , which is not 10. So $x = 13$ fails.

Correct: divide both sides by 2 first then $x - 3 = 5$ then $x = 8$ .

Check: $2 (8 - 3) = 2 \times 5 = 10$ . It works.

Move: divide both sides by 2, then add 3. Why: keep both sides equal; substitute your answer to catch a wrong root.

We Do

Try this step

Solve $3 (x + 2) = 18$ . Which value of $x$ is correct? (Try a tempting wrong root first if you like.)

You Do

On your own

Solve $4 (x - 1) = 20$ . What is $x$ ?

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