Equations with Unknowns on Both Sides Flashcards

All 6 cards in this deck

What are the steps to solve an equation with the unknown on both sides?

e.g. $5x - 2 = 3x + 6$

1. Subtract $3x$ from both sides: $2x - 2 = 6$
2. Add 2 to both sides: $2x = 8$
3. Divide by 2: $x = 4$

When the unknown is on both sides, which side should you collect the unknown terms on?

The side with the larger coefficient of the unknown, so you avoid a negative coefficient.
e.g. in $3x + 1 = 7x - 5$, collect the $x$ terms on the right.

What are the steps to solve an equation with brackets on both sides?

e.g. $2(x + 3) = 4(x - 1)$

1. Expand both brackets: $2x + 6 = 4x - 4$
2. Collect $x$ terms on one side and numbers on the other: $10 = 2x$
3. Divide by 2: $x = 5$

True or false? To remove the $-x$ from the right-hand side of $5x - 14 = 52 - x$ you add $x$ to both sides.

True. It gives $6x - 14 = 52$.

What do you do if collecting the unknowns leaves a negative coefficient?

e.g. $-2x = 6$

Divide both sides by the negative number: $x = -3$.

How can you check that your solution to an equation is correct?

Substitute the value back into the original equation and check both sides give the same value.