Linear Equations Flashcards

All 17 cards in this deck

What is the balance rule for solving equations?

Whatever you do to one side, you must do exactly the same to the other side.

What are the steps to solve a two-step equation?

e.g. $5p + 7 = 22$

1. Subtract 7 from both sides: $5p = 15$
2. Divide both sides by 5: $p = 3$

How do you find an approximate solution of a linear equation from a graph?

e.g. $2x + 1 = 4$

Draw $y = 2x + 1$ and $y = 4$, then read off the $x$-coordinate where the lines cross.

What are the steps to solve an equation containing brackets by expanding?

e.g. $3(x - 4) = 12$

1. Expand the bracket: $3x - 12 = 12$
2. Add 12 to both sides: $3x = 24$
3. Divide by 3: $x = 8$

What is the alternative first step for an equation like $4(x - 5) = 18$, instead of expanding?

Divide both sides by 4: $x - 5 = 4.5$, so $x = 9.5$

True or false? To expand $5(2m - 6)$ you multiply only the first term inside the bracket by 5.

False. Every term inside the bracket is multiplied: $10m - 30$.

What are the steps to solve an equation with an algebraic fraction?

e.g. $\frac{x}{3} + 2 = 5$

1. Subtract 2 from both sides: $\frac{x}{3} = 3$
2. Multiply both sides by 3: $x = 9$

How do you remove the fraction when the whole expression is over a number?

e.g. $\frac{x + 1}{2} = 5$

Multiply both sides by the denominator: $x + 1 = 10$, so $x = 9$.

True or false? A correct first step for $\frac{3y}{4} = 12$ is to multiply both sides by 4.

True. It gives $3y = 48$, then $y = 16$.

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.

Which operations undo each other when solving a one-step equation?

Add undoes subtract, and multiply undoes divide.
e.g. to solve $\frac{x}{4} = 3$ you multiply both sides by 4.

What is the first step when the unknown is added to itself several times on one side?
e.g. $x + x + x = 51$

Collect like terms.
$x + x + x = 3x$, so the equation becomes $3x = 51$.